Q) 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 x 8 cm x 5 cm. These milk packets are then packed in cuboidal
cartons of dimensions 30 cm x 32 cm x 15 cm.

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

Ans: 

(i) Volume of a carton:

Since the volume of a cuboid is given by: V = L x B X H

It is given that for Box, L = 30 cm, B = 32 cm and H = 15 cm

∴ V_Box = 30 x 32 x 15 = 14400 cm³

Therefore, volume of the cuboidal carton is 14,400 cm³.

(ii) TSA of a Milk Pack:

Since, Total Surface Area of a cuboid = 2 (LB + BH + LH)

It is given that for Box, L = 8 cm, B = 5 cm and H = 15 cm

∴ TSA_Pack = 2(8 x 5 + 5 x 15 + 8 x 15) = 2 (40 + 75 + 120) = 470 cm²

Therefore, the total surface area of a milk pack is 470 cm²

(iii) No. of packs in a carton:

Let’s calculate volume of a milk pack

Since, Volume of a cuboid is given by: V = L x B X H

It is given that for a milk pack, L = 8 cm, B = 5 cm and H = 15 cm

∴ V_Pack = 8 x 5 x 15 = 600 cm³

Since these milk packs need to be kept inside the box,

∴ No. of Milk pack kept inside the Carton Box =

= = 24 units

Therefore, 24 milk packs can be kept in the carton box.

(iv) Milk quantity in the cup:

By milk quantity in the cup means we need to calculate capacity or volume of the cup.

Since the Cup is cylindrical and volume of a cylinder is given by: π r² h

The cup dimensions from the figure are: radius r = 5 cm and height H = 7 cm

Therefore, Volume of the cup, V_Cup = π (5)² (7)

= x 25 x 7 = 22 x 25 = 550 cm³

Therefore, the cup can hold 550 cm³ milk.

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