Question

If the radius of a sphere is increased by 20 %, by what per cent does its volume
increase ?
​

Answer 1

Let the original radius= r

Thus new radius =

• 20%r + r
• 1r/5 + r
• 6r/5

(vol. = 4/3 πr³)

Thus

original volume = V1

V1 = 4/3 π r³

Thus new volume = V2

V2 = 4/3 π (6r/5)³

V2 = 4/3 π 216r³/125

Thus change in volume;

• V2 - V1
• 4/3πr³ (216/125 - 1)
• 4/3πr³ (91/125)

Thus % increase =

• [ 4/3 π r³ (91/125) ] ÷ [ 4/3 π r³ ] × 100
• 91/125 × 100
• 91/25 × 20
• 91/5 × 4
• 364/5
• 72.8%

#answerwithquality

#BAL