Surface Areas And Volumes

CBSE Class 10 — Maths — Previous Year Questions

Q1.VSA1 mark(2020)Easy

Two cones have their heights in the ratio $1:3$ and radii in the ratio $3:1$. What is the ratio of their volumes?

Q2.VSA1 mark(2020)Easy

Two right circular cones have their heights in the ratio $1:3$ and radii in the ratio $3:1$, what is the ratio of their volumes?

Q3.VSA1 mark(2020)Easy

A spherical metal ball of radius 8 cm is melted to make 8 smaller identical balls. The radius of each new ball is ________ cm.

Q4.MCQ1 mark(2020)Easy

The radius of a sphere (in cm) whose volume is $12\pi$ cm${}^3$, is

Q5.MCQ1 mark(2023)Easy

Curved surface area of a cylinder of height 5 cm is $94.2$ cm${}^2$. Radius of the cylinder is (Take $\pi =3.14$)
(A) $2$ cm
(B) $3$ cm
(C) $2.9$ cm
(D) $6$ cm

Q6.MCQ1 mark(2023)Easy

The curved surface area of a cone having height 7 cm and radius 7 cm, is
(A) $528$ cm${}^2$
(B) $1056$ cm${}^2$
(C) $550$ cm${}^2$
(D) $500$ cm${}^2$

Q7.MCQ1 mark(2023)Easy

What is the total surface area of a solid hemisphere of diameter '$d$'?
(a) $3\pi d^2$
(b) $2\pi d^2$
(c) $\frac{1}{2}\pi d^2$
(d) $\frac{3}{4}\pi d^2$

Q8.Case-Study1 mark(2023)Easy

Case Study - 2

In a coffee shop, coffee is served in two types of cups. One is cylindrical in shape with diameter 7 cm and height 14 cm and the other is hemispherical with diameter 21 cm.



Based on the above, answer the following questions:

(i) Find the area of the base of the cylindrical cup.

Q9.Case-Study1 mark(2023)Easy

Case Study - 2 (continued)

Refer to the coffee cups described in Q37.

(ii)(a) What is the capacity of the hemispherical cup?

Q10.Case-Study1 mark(2023)Easy

Case Study - 2 (continued)

Refer to the coffee cups described in Q37.

(ii)(b) Find the capacity of the cylindrical cup.

Q11.MCQ1 mark(2023)Easy

Water in a river which is $3$ m deep and $40$ m wide is flowing at the rate of $2$ km/h. How much water will fall into the sea in $2$ minutes?

Q12.Case-Study1 mark(2023)Easy

A golf ball is spherical with about $300-500$ dimples that help increase its velocity while in play. Golf balls are traditionally white but available in colours also. In the given figure, a golf ball has diameter $4.2$ cm and the surface has $315$ dimples (hemi-spherical) of radius $2$ mm.



Based on the above, answer the following questions:

(i) Find the surface area of one such dimple.

Q13.Case-Study1 mark(2023)Easy

(ii) Find the volume of the material dug out to make one dimple.

Q14.MCQ1 mark(2023)Easy

The volume of a right circular cone whose area of the base is $156$ cm${}^2$ and the vertical height is $8$ cm, is

Q15.MCQ1 mark(2024)Medium

A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres taken together, is:

Q16.MCQ1 mark(2024)Medium

The volume of the largest right circular cone that can be carved out from a solid cube of edge $2$ cm is:

Q17.Assertion-Reason1 mark(2024)Medium

**Assertion (A):** Two cubes each of edge length $10$ cm are joined together. The total surface area of newly formed cuboid is $1200$ cm${}^2$.

**Reason (R):** Area of each surface of a cube of side $10$ cm is $100$ cm${}^2$.

Q18.MCQ1 mark(2024)Easy

The ratio of total surface area of a solid hemisphere to the square of its radius is:

Q19.Assertion-Reason1 mark(2025)Easy

Assertion (A): If we join two hemispheres of same radius along their bases, then we get a sphere.

Reason (R): Total Surface Area of a sphere of radius $r$ is $3\pi r^2$.

Q20.MCQ1 mark(2025)Easy

If the volumes of two cubes are in the ratio $8:125$, then the ratio of their surface areas is:

Q21.MCQ1 mark(2025)Easy

On the top face of the wooden cube of side 7 cm, hemispherical depressions of radius 0.35 cm are to be formed by taking out the wood. The maximum number of depressions that can be formed is:

Q22.VSA2 marks(2020)Easy

The volume of a right circular cylinder with its height equal to the radius is $25\frac{1}{7}$ cm${}^3$. Find the height of the cylinder. (Use $\pi =\frac{22}{7}$)

Q23.VSA2 marks(2020)Medium

Read the following passage and answer the questions given at the end:

Students of Class XII presented a gift to their school in the form of an electric lamp in the shape of a glass hemispherical base surmounted by a metallic cylindrical top of same radius 21 cm and height 3.5 cm. The top was silver coated and the glass surface was painted red.

(i) What is the cost of silver coating the top at the rate of ₹5 per 100 cm${}^2$?
(ii) What is the surface area of glass to be painted red?

Q24.VSA2 marks(2020)Easy

In Figure-6, a tent is in the shape of a cylinder surmounted by a conical top. The cylindrical part is 2.1 m high and conical part has slant height 2.8 m. Both the parts have same radius 2 m. Find the area of the canvas used to make the tent. (Use $\pi =\frac{22}{7}$)

Q25.VSA2 marks(2020)Easy

$2$ cubes, each of volume $125$ cm${}^3$, are joined end to end. Find the surface area of the resulting cuboid.

Q26.VSA2 marks(2022)Medium

A solid metallic sphere of radius $10.5$ cm is melted and recast into a number of smaller cones, each of radius $3.5$ cm and height $3$ cm. Find the number of cones so formed.

Q27.VSA2 marks(2022)Easy

A solid piece of metal in the form of a cuboid of dimensions $11$ cm $\times$ $7$ cm $\times$ $7$ cm is melted to form '$n$' number of solid spheres of radii $\frac{7}{2}$ cm each. Find the value of $n$.

Q28.VSA2 marks(2022)Medium

The curved surface area of a right circular cylinder is $176$ sq cm and its volume is $1232$ cu cm. What is the height of the cylinder?

Q29.VSA2 marks(2022)Easy

The largest sphere is carved out of a solid cube of side 21 cm. Find the volume of the sphere.

Q30.Case-Study2 marks(2022)Medium

Khurja is a city in the Indian state of Uttar Pradesh famous for the pottery. Khurja pottery is traditional Indian pottery work which has attracted Indians as well as foreigners with a variety of teacups, crockery and ceramic tile works. A huge portion of the ceramics used in the country is supplied by Khurja and is also referred as 'The Ceramic Town'.

One of the private schools of Bulandshahr organised an Educational Tour for class 10 students to Khurja. Students were very excited about the trip. Following are the few pottery objects of Khurja.





Students found the shapes of the objects very interesting and they could easily relate them with mathematical shapes viz sphere, hemisphere, cylinder etc. Maths teacher who was accompanying the students asked following questions:

(a) The internal radius of hemispherical bowl (filled completely with water) in I is 9 cm and radius and height of cylindrical jar in II is 1.5 cm and 4 cm respectively. If the hemispherical bowl is to be emptied in cylindrical jars, then how many cylindrical jars are required?

Q31.Case-Study2 marks(2022)Medium

(b) If in the cylindrical jar full of water, a conical funnel of same diameter and same height is immersed, then how much water will flow out of the jar?

Q32.Case-Study2 marks(2023)Easy

Case Study - 2 (continued)

Refer to the coffee cups described in Q37.

(iii) What is the curved surface area of the cylindrical cup?

Q33.Case-Study2 marks(2023)Medium

(iii) (a) Find the total surface area exposed to the surroundings.

Q34.Case-Study2 marks(2023)Medium

(iii) (b) Find the volume of the golf ball.

Q35.SA3 marks(2020)Hard

A cone of base radius 4 cm is divided into two parts by drawing a plane through the mid-point of its height and parallel to its base. Compare the volume of the two parts.

Q36.SA3 marks(2020)Easy

500 persons are taking dip into a cuboidal pond which is 80 m long and 50 m broad. What is the rise of water level in the pond, if the average displacement of the water by a person is 0.04 m${}^3$?

Q37.SA3 marks(2023)Medium

A room is in the form of cylinder surmounted by a hemi-spherical dome. The base radius of hemisphere is one-half the height of cylindrical part. Find total height of the room if it contains $\left(\frac{1408}{21}\right)m^3$ of air. Take $\left(\pi =\frac{22}{7}\right)$

Q38.SA3 marks(2023)Hard

An empty cone is of radius 3 cm and height 12 cm. Ice-cream is filled in it so that lower part of the cone which is $\left(\frac{1}{6}\right)$ of the volume of the cone is unfilled but hemisphere is formed on the top. Find the volume of the ice-cream. (Take $\pi =3.14$)

Q39.SA3 marks(2024)Medium

The difference between the outer and inner radii of a hollow right circular cylinder of length 14 cm is 1 cm. If the volume of the metal used in making the cylinder is $176$ cm${}^3$, find the outer and inner radii of the cylinder.

Q40.SA3 marks(2025)Medium

A room is in the form of a cylinder surmounted by a hemispherical dome. The base radius of the hemisphere is half of the height of the cylindrical part. If the room contains $\frac{1400}{3}$ m${}^3$ of air, find the height of the cylindrical part. (Use $\pi =\frac{22}{7}$)

Q41.LA4 marks(2020)Medium

A bucket in the form of a frustum of a cone of height $30$ cm with radii of its lower and upper ends as $10$ cm and $20$ cm respectively. Find the capacity of the bucket. Also find the total cost of milk that can completely fill the bucket at the rate of Rs. $40$ per litre. $\left(\text{Use }\pi =\frac{22}{7}\right)$

Q42.LA4 marks(2020)Medium

Find the curved surface area of the frustum of a cone, the diameters of whose circular ends are 20 m and 6 m and its height is 24 m.

Q43.LA4 marks(2020)Medium

A solid iron cuboidal block of dimensions 4.4 m $\times$ 2.6 m $\times$ 1 m is cast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.

Q44.LA4 marks(2020)Medium

A bucket open at the top has top and bottom radii of circular ends as 40 cm and 20 cm respectively. Find the volume of the bucket if its depth is 21 cm. Also find the area of the tin sheet required for making the bucket. (Use $\pi =\frac{22}{7}$)

Q45.LA4 marks(2020)Medium

A solid toy is in the form of a hemisphere surmounted by a right circular cone of same radius. The height of the cone is $10$ cm and the radius of its base is $7$ cm. Determine the volume of the toy. Also find the area of the coloured sheet required to cover the toy.

(Use $\pi =\frac{22}{7}$ and $\sqrt{149}=12.2$)

Q46.LA4 marks(2022)Medium

From a solid cylinder of height $30$ cm and radius $7$ cm, a conical cavity of height $24$ cm and same radius is hollowed out. Find the total surface area of the remaining solid.

Q47.LA4 marks(2022)Medium

Water in a canal, $8$ m wide and $6$ m deep, is flowing with a speed of $12$ km/hour. How much area will it irrigate in one hour, if $0.05$ m of standing water is required?

Q48.Case-Study4 marks(2022)Medium

Case Study - 2:

A 'circus' is a company of performers who put on shows of acrobats, clowns etc. to entertain people started around $250$ years back, in open fields, now generally performed in tents.

One such 'Circus Tent' is shown below.



The tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of cylindrical part are $9$ m and $30$ m respectively and height of conical part is $8$ m with same diameter as that of the cylindrical part, then find

(1) the area of the canvas used in making the tent;

(2) the cost of the canvas bought for the tent at the rate Rs. $200$ per sq m, if $30$ sq m canvas was wasted during stitching.

Q49.Case-Study4 marks(2024)Medium

The word 'circus' has the same root as 'circle'. In a closed circular area, various entertainment acts including human skill and animal training are presented before the crowd.

A circus tent is cylindrical upto a height of $8$ m and conical above it. The diameter of the base is $28$ m and total height of tent is $18.5$ m.



Based on the above, answer the following questions:
(i) Find slant height of the conical part.
(ii) Determine the floor area of the tent.
(iii) (a) Find area of the cloth used for making tent.

**OR**

(iii) (b) Find total volume of air inside an empty tent.

Q50.Case-Study4 marks(2024)Medium

The word 'circus' has the same root as 'circle'. In a closed circular area, various entertainment acts including human skill and animal training are presented before the crowd.

A circus tent is cylindrical upto a height of $8$ m and conical above it. The diameter of the base is $28$ m and total height of tent is $18.5$ m.



Based on the above, answer the following questions:
(i) Find slant height of the conical part.
(ii) Determine the floor area of the tent.
(iii) (b) Find total volume of air inside an empty tent.

Q51.Case-Study4 marks(2024)Medium

Tamper-proof tetra-packed milk guarantees both freshness and security. This milk ensures uncompromised quality, preserving the nutritional values within and making it a reliable choice for health-conscious individuals.



$500$ mL milk is packed in a cuboidal container of dimensions $15$ cm $\times$ $8$ cm $\times$ $5$ cm. These milk packets are then packed in cuboidal cartons of dimensions $30$ cm $\times$ $32$ cm $\times$ $15$ cm.

Based on the above given information, answer the following questions:
(i) Find the volume of the cuboidal carton.
(ii) (a) Find the total surface area of a milk packet.

**OR**

(ii) (b) How many milk packets can be filled in a carton?
(iii) How much milk can the cup (as shown in the figure) hold?

Q52.Case-Study4 marks(2024)Medium

Tamper-proof tetra-packed milk guarantees both freshness and security. This milk ensures uncompromised quality, preserving the nutritional values within and making it a reliable choice for health-conscious individuals.



$500$ mL milk is packed in a cuboidal container of dimensions $15$ cm $\times$ $8$ cm $\times$ $5$ cm. These milk packets are then packed in cuboidal cartons of dimensions $30$ cm $\times$ $32$ cm $\times$ $15$ cm.

Based on the above given information, answer the following questions:
(i) Find the volume of the cuboidal carton.
(ii) (b) How many milk packets can be filled in a carton?
(iii) How much milk can the cup (as shown in the figure) hold?

Q53.Case-Study4 marks(2025)Medium

**Case Study - 3**

A skilled carpenter decided to craft a special rolling pin for the local baker. He carefully joined three cylindrical pieces of wood — two small ones on the ends and one larger in the centre to create a perfect tool. The baker loved the rolling pin, as it rolled out the smoothest dough for breads and pastries.



The length of the bigger cylindrical part is 12 cm and diameter is 7 cm and the length of each smaller cylindrical part is 5 cm and diameter is $2.1$ cm.

Based on the above information, answer the following questions:

(i) Find the volume of the bigger cylindrical part.

(ii) Find the curved surface area of the bigger cylindrical part.

(iii) (a) Find the ratio of the volume of the bigger cylindrical part to the total volume of the two smaller (identical) cylindrical parts.

**OR**

(iii) (b) Find the sum of the curved surface areas of the two identical smaller cylindrical parts.

Q54.LA5 marks(2023)Medium

A student was asked to make a model shaped like a cylinder with two cones attached to its ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its total length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model.

Q55.LA5 marks(2023)Medium

A solid is in the shape of a right-circular cone surmounted on a hemisphere, the radius of each of them being $7$ cm and the height of the cone is equal to its diameter. Find the volume of the solid.

Q56.LA5 marks(2024)Easy

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the figure. If the height of the cylinder is 5.8 cm and its base is of radius 2.1 cm, find the total surface area of the article.

Q57.LA5 marks(2025)Medium

A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm, are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.

Q58.LA5 marks(2025)Hard

A wooden cubical die is formed by forming hemispherical depressions on each face of the cube such that face 1 has one depression, face 2 has two depressions and so on. The sum of number of hemispherical depressions on opposite faces is always 7. If the edge of the cubical die measures 5 cm and each hemispherical depression is of diameter 1.4 cm, find the total surface area of the die so formed.