NCERT Solutions for Class 10 Maths Chapter 13

Important NCERT Questions

Surface areas and Volumes,

NCERT Books for Session 2022-2023

CBSE Board and UP Board Others state Board

EXERCISE 13.4

Page No:257

Questions No:4

# A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Find the cost of the milk which can completely fill the container, at the rate of ` 20 per litre. Also find the cost of metal sheet used to make the container, if it costs ` 8 per 100 cm2. (Take π = 3.14)

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Radius of upper part of container (r₁) = 20 cm

Radius of lower part of container (r₂) = 8 cm

Height of container (h) = 16 cm

Slant height of container = √((r₁ – r₂)² + h²)

= √((20 – 8)² + 16²) = √(144+256) = √400 = 20 cm

Capacity of container = Volume of frustum = 1/3πh(r²₁ + r²₂ + r₁r₂)

= 1/3 × 3.14 × 16 × (20² + 8² + 20 × 8 ) = 1/3 × 3.14 × 16 × (400 + 64 + 160)

= 1/3 × 3.14 × 16 × 624 = 104449.92 cm³ = 10.45 litres.

Cost of 1 litre of milk = Rs 20

Therefore, the cost of 10.45 litres of milk = 10.45 × Rs 20 = Rs 209

The area of metal sheet used to make the container

= π(r₁+ r₂)l + π(r₂)²

= π(20 + 8) 20 + π(8)²

= 560π + 64 π = 624 π cm²

Cost of 100 cm² metal sheet = Rs 8

Cost of cm² metal sheet = Rs 8/100

Therefore, the cost of 624 π cm² metal sheet = Rs 8/100 × 624π = Rs 8/100 × 624 × 3.14 = Rs 156.75

Hence, the cost of the milk which can completely fill the container is Rs 209 and the cost of metal sheet used to make the container is Rs 156.75.