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-cons

Question

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.

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

Accepted Answer

Step 1: (i) Volume of cuboidal carton $= 30 	imes 32 	imes 15 = 14400$ cm$^3$
Step 2: (ii)(a) TSA of milk packet $= 2(15 	imes 8 + 8 	imes 5 + 5 	imes 15) = 2(120 + 40 + 75) = 470$ cm$^2$
Step 3: (iii) Capacity of the cup $= \frac{22}{7} 	imes 5 	imes 5 	imes 7 = 550$ cm$^3$ or $550$ mL

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