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.

500 ml milk is packed in a cuboidal container of dimensions 15 cm × 8 cm × 5 cm. These milk packets are then packed in cuboidal cartons of dimensions 30 cm × 32 cm × 15 cm.

Based on the above-given information, answer the following questions:

i. Find the volume of the cuboidal carton. (1)

ii. a. Find the total surface area of the milk packet. (2)

OR

b. How many milk packets can be filled in a carton? (2)

iii. How much milk can the cup (as shown in the figure) hold? (1)

Answer 1

(i) Volume of the cuboidal carton

The formula for the volume of a cuboid is:

V = length × breadth × height

length = 30 cm, breadth = 32 cm, height = 15 cm

V = 30 × 32 × 15

V = 14400 cm³

(ii) a. Total Surface Area of the Milk Packet

TSA = 2(lb + bh + hl)

l = 15 cm, b = 8 cm, h = 5 cm

TSA = 2 × (15 × 8 + 8 × 5 + 5 × 15)

TSA = 2 × (120 + 40 + 75)

TSA = 2 × 235

TSA = 470 cm²

(ii) b. Number of Milk Packets in the Carton

Step 1: Volume of a single milk packet

V = l × b × h

V = 15 × 8 × 5

V = 600 cm³

Step 2: Number of packets

Number of packets = `"Volume of carton"/"Volume of one packet"`

= `14400/600`

= 24

(iii) Volume of the Cup

The given cup in the image is cylindrical. The volume of a cylinder is given by:

V = πr²h

From the image:

• Radius r = 5
• Height h is not provided in the image. To calculate the exact volume, we need the height of the cup.