The diameter of two circular ends of a bucket are 44 cm and 24 cm, and the height of the bucket is 35 cm. The capacity of the bucket is
Given: Diameter of two circular ends of a bucket are 44 cm and 24 cm, and the height of the bucket is 35 cm.
Bucket is in the shape of frustum.
Let V be the Volume of the Bucket(Frustum)
Volume of the frustum is given by: × h × (R2 + r2 + Rr) (here r and R are the radii of smaller and larger circular ends respectively)
∴ V = × h × (R2 + r2 + R × r)
⇒ V = × 35 × (222 + 122 + 22 × 12) (diameters are 44 and 24 cm, ∴ their radii are 22cm and 12cm respectively)
⇒ V = × 35 × (484 + 144 + 264) =
× 35 × (892)
⇒ V = × 35 × (892) = 32706.6 cm3 = 32.7 litres (∵ 1000cm3 = 1 litre)
∴ The capacity of the bucket is: 32.7 litres