Question

E 10
On increasing the radius of a sphere by 10%, find the percentage
increase in its volume.​

Answer 1

Answer:

Percentage increase = 33.1%

Explaination

let the original radius of the sphere is = x

therefore volume = 3/4 π R³

v = 3/4 × π × x³ _____ (1)

Now, increased radius = 110/100 x

volume ( v' ) = 3/4 × π × (11/10x)³

v' = 3/4 × π × 1331/1000 x ³

from =n(1) we have,

v' = v × 1331 / 1000. _______(2)

Percentage change =

change in volume - original volume /original volume × 100

= v'- v / v ×100

From =n(2) ,

= (v × 1331 /1000 - v )/ v × 100

= (1331v - 1000v / 1000 ) ÷ v × 100

= ( 331v /1000 ) / v × 100

= 331×100/1000

= 33.1 %

Hence Percentage increase = 33.1%