The diameters of the lower and upper ends of a bucket in the former of a cone are 16cm and 30 cm respectively. If it's height is 24cm. Find the area of the metalled sheet use to make a bucket.
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Answer: 2078.68 cm²
Step by step explanation:
Given :
Diameter of upper end of bucket = 30 cm
Radius of the upper end of the frustum of cone (r1) = 15 cm
Diameter of lower end of bucket = 16 cm
Radius of the lower end of the frustum of cone(r2) = 8 cm
Height of the frustum of Cone (h) = 24 cm
Slant height of bucket (L)= √(h² + (r1 - r2)²)
L =√(24² + (15 - 8)²) = √576 + 7²
L =√(576+(49)) = √625 = 25 cm
L = 25 cm
Area of metal sheet require to make it = π(r1 + r2)L + πr2²
= 3.14(15 + 8) × 26 + π(8)²
= 3.14 × 23 × 26 + 64 × 3.14
= 1877.72 + 200.96
= 2078.68 cm²
Area of metal sheet require to make it = 2078.68 cm²
Hence, the Area of metal sheet used to make the bucket is 2078.68 cm².
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