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.
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