The radii of the ends of a bucket 30cm high are 21cm and 7cm find its capacity in litres and the amount of sheet required to make this bucket
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Answer:
The Capacity of the bucket is 20.02 litres and Total area of the metal sheet required to make the bucket is 3067 cm².
Step-by-step explanation:
SOLUTION :
Given :
Height of a bucket, h = 30 cm
Radius of the top of a bucket, R = 21 cm
Radius of the bottom of a bucket,r = 7 cm
Capacity of the bucket = ⅓ πh(R² + r² + Rr)
= ⅓ × 22/7 × 30 (21² + 7² + 21 × 7)
= 220/7 (441 + 49 + 147)
= 220/7 × 637
= 220 × 91
= 20,020 cm³
= 20,020/1000 litres
[1 cm³ = 1/1000 litres]
= 20.02 litres
Capacity of the bucket = 20.02 litres
Slant height of the bucket, l = √h² + (R - r)²
l = √30² +(21 -7)²
l = √900 + 14² = √900 + 196 = √1096
l = 33.1 cm
Total area of the metal sheet required to make the bucket = πl(R + r) + πr²
= π× 33.1 (21 + 7) + π ×7²
= π × 33.1 × 28 + π × 49
= π × 926.8 + 49π
= π(926.8 + 49)
= 22/7 × 975.8
= 22 × 139.4
= 3,066.8 ≈ 3067 cm²
Total area of the metal sheet required to make the bucket = 3067 cm²
Hence, the Capacity of the bucket is 20.02 litres and Total area of the metal sheet required to make the bucket is 3067 cm².
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