**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 cm ^{3}**

**Therefore, volume of the cuboidal carton is 14,400 cm ^{3}.**

**(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 cm ^{2}**

**Therefore, the total surface area of a milk pack is 470 cm ^{2}**

**(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 cm^{3}

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 r^{2} 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 cm^{3}

**Therefore, the cup can hold 550 cm ^{3} milk.**

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