A bucket is in the form of a frustum of a cone with a capacity of 12308.8 cm3 of water. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket. (Use π = 3.14.)
Upper end radius of frustum/bucket = R = 20 cm
Lower end radius of frustum/bucket =r = 12 cm
Height of the frustum/bucket be ‘h’ cm
And we know,
The capacity of bucket = Volume of the bucket
And, Volume of bucket = Volume of Frustum
Volume of frustum/bucket = V = 12308.8 cm3
∴ Capacity of bucket = Volume of frustum
⇒Volume of frustum
Where R = Radius of larger or upper end and r = Radius of smaller or lower end and h = height of frustum π = 3.14
(putting the values)
⇒ 3.14 × h × (144 + 400 + 240) = 12308.8 × 3
⇒ 3.14 × h × 784 = 36926.4
⇒ 2461.76 × h = 36926.4
⇒ h = 36926.4/2461.76
∴ h = 15 cm
The height of the bucket is 15 cm.