The diameter of lower and upper ends of bucket in the form of frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, find: 1. The capacity of the bucket 2. The area of the metal sheet used to made the bucket.
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It is given that
d1 = 30 cm so r1 = 30 / 2 = 15 cm
d2 = 10 cm so r2 = 10 / 2 = 5 cm
Height = 24 cm
l = √h² + (r1 - r2)²
l = √576 + 100
l = √676
l = 26
Volume of frustum
= 1/3πh ( r1² + r2² + r1*r2)
= 1/3 × 22/7 × 24 ( (15)² + (5)² + 15*5)
= 22/7 × 8 ( 225 + 25 + 75)
= 22/7 × 8 ( 325)
= 57200 / 7
= 8171.428cm ³
= 8171428 Litre
Area of metal sheet used
= CSA of frustum + Base of Frustum
= πl ( r1 + r2) + πr2²
= π [( 15 + 5 ) × 26 + (5)² ]
= π ( 20 * 26 + 25)
= π ( 520 + 25)
= 22/7 × 545
= 1712.85 cm²
= 1712.8 cm² (approx.)
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d1 = 30 cm so r1 = 30 / 2 = 15 cm
d2 = 10 cm so r2 = 10 / 2 = 5 cm
Height = 24 cm
l = √h² + (r1 - r2)²
l = √576 + 100
l = √676
l = 26
Volume of frustum
= 1/3πh ( r1² + r2² + r1*r2)
= 1/3 × 22/7 × 24 ( (15)² + (5)² + 15*5)
= 22/7 × 8 ( 225 + 25 + 75)
= 22/7 × 8 ( 325)
= 57200 / 7
= 8171.428cm ³
= 8171428 Litre
Area of metal sheet used
= CSA of frustum + Base of Frustum
= πl ( r1 + r2) + πr2²
= π [( 15 + 5 ) × 26 + (5)² ]
= π ( 20 * 26 + 25)
= π ( 520 + 25)
= 22/7 × 545
= 1712.85 cm²
= 1712.8 cm² (approx.)
Hope you like it please mark as brainliest and follow me if you like my answer.
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