Question

Volume of a sphere is given by V=4/3πr³ , where r is its radius . If radius changes by 1.2% , then find the change in the volume ?

Answer 1

Volume goes with the cube of linear scaling.

`1.012^3=1.036433728,` so volume increases about `3.64%.`

Answer 2

The change in volume is proportional to the original volume and approximately equal to `0.0364 * "Initial Volume"`.

Explanation:

Let `V_"new"` be the volume of the new sphere of the radius change and let `r_"new"` be the new radius.

`r_"new" = r+1.2%"of "r=r+1.2/100 r=r(1+1.2/100)=101.2/100r`

`V_"new" = (4pir_"new"^3)/3=(4pi(101.2/100)^3r^3)/3=(101.2/100)^3 (4pir^3)/3`

`V_"new" = (101.2/100)^3 V`

`"Change" = V_"new" - V = V[(101.2/100)^3-1]~~0.0364V`