A solid is in the shape of a cylinder surmounted on a hemisphere. If the diameter and the total height of the solid are 21 cm and 25.5 cm respectively, then find its volume.
Let r and h be radius and height of the cylinder respectively.
Given, diameter of the hemisphere = 21 cm
So, radius of hemisphere (r) = 212 = 10.5 cm
Given, height of the solid shape = 25.5 cm
Also, radius of hemisphere + height of the cylinder = 25.5 cm
So, 10.5 + h = 25.5
h = 25.5 - 10.5
h = 15 cm
To find the volume of the solid shape we have to find the sum of volume of hemisphere and volume of cylinder.
Volume of solid shape
= Volume of hemisphere + Volume of cylinder
= 23πr3+πr2h
= πr2[23r+h]
= 227×(10.5)2×[23×10.5+15]
= 22 x 1.5 x 10.5 x [ 2 x 3.5 + 15]
= 346.5 x 22
= 7623 cm3