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.

Question

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

π = \frac{22}{7}

and

149 = 12.2

)

$Hemisphere surmounted by cone, height 10 cm, radius 7 cm$

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

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Accepted Answer

Step 1: Volume of toy $= \frac{2}{3}\pi r^3 + \frac{1}{3}\pi r^2 h = \frac{2}{3} 	imes \frac{22}{7} 	imes (7)^3 + \frac{1}{3} 	imes \frac{22}{7} 	imes (7)^2 	imes 10$
Step 2: $= \frac{2}{3} 	imes 22 	imes 49 + \frac{1}{3} 	imes 22 	imes 7 	imes 10 = \frac{2156}{3} + \frac{1540}{3} = \frac{3696}{3} = 1232$ cm$^3$
Step 3: Slant height $l = \sqrt{h^2 + r^2} = \sqrt{10^2 + 7^2} = \sqrt{149} = 12.2$ cm. Area of sheet $= 2\pi r^2 + \pi r l = 2 	imes \frac{22}{7} 	imes 49 + \frac{22}{7} 	imes 7 	imes 12.2$
Step 4: $= 308 + 22 	imes 12.2 = 308 + 268.4 = 576.4$ cm$^2$

Question

Solution