Question

The following figure represents a solid consisting of a cylinder surmounted by a cone at one end and a hemisphere at the other end. Given that common radius = 3.5 cm, the height of the cylinder = 6.5 cm and the total height = 12.8 cm, calculate the volume of the solid, correct to the nearest cm³.

Answer 1

Given :
Common radius r = 3.5 cm
Height of cylinder h_c = 6.5 cm
Total height (length) = 12.8 cm

`π = 22/7`

The solid = hemisphere + cylinder + cone

Step 1: Find the height of the cone

Length of hemisphere along axis = r = 3.5 cm

h_cone ​= 12.8 − 6.5 − 3.5

= 2.8 cm

Step 2: Volume of each part

(i) Volume of a cylinder

Vc​ = `πr^2hc ​= 22/7 xx (3.5)^2 xx 6.5`

= `22/7 xx 12.25 xx 6.5 = 250.25 cm^3`

(ii) Volume of a hemisphere

`V_h = 2/3 πr^3 = 2/3 xx 22/7 xx (3.5)^3`

= `2/3 xx 22/7 xx 42.875 = 89.83 cm^3`

(iii) Volume of cone

`Vco = 1/3 πr^2h_"cone"`

= `1/3 xx 22/7 xx (3.5)^2 xx 2.8`

= `1/3 xx 22/7 xx 12.25 xx 2.8`

= 35.93 cm³

Step 3: Total volume

V = Vc​ + Vh​ + Vco ​

= 250.25 + 89.83 + 35.93

= 376.01 cm³

Volume of the solid (nearest cm³) = 376 cm³