Question

Find the volume of a sphere whose surface area is 154 cm2.

 

Answer 1

In the given problem, we have to find the volume of a sphere whose surface area is given.

So, let us first find the radius of the given sphere.

Surface area of the sphere (S) = 154 cm²

Let the radius of the sphere be r cm

Now, we know that surface area of the sphere = `4pir^2`

So,

`154 = 4(22/7)(r)^2`

`  r^2 = ((154)(7))/((4)(22))`

` r^2 = 12.25`  

Further, solving for r

`r = sqrt(12.25)`

r= 3.5

Therefore, the radius of the given sphere is 3.5 cm.

Now, the volume of the sphere = `4/3 pi r^3`

`=(4/3)(22/7)(3.5)^3`

=179.66 cm²

Therefore, the volume of the given sphere is 179.66 cm² .