Question

The Volume of a sphare is 28/3 times the surface area calculate The surface area and the Volume of the sphere, correct to the nearest whole number.​

Answer 1

Given:

Volume of a sphere is
`(28)/(3)` times the surface area.

To find:

The surface area and the volume of the sphere.

Solution:

Volume of a sphere:

`V=(4)/(3)\pi r^3` ...(i)

Surface area of a sphere:

`A=4\pi r^2` ...(ii)

Where, r is the radius of the sphere.

Volume of a sphere is
`(28)/(3)` times the surface area.

`V=(28)/(3)* A`

`(4)/(3)\pi r^3=(28)/(3)* 4\pi r^2`

Multiply both sides by 3.

`4\pi r^3=112\pi r^2`

`(\pi r^3)/(\pi r^2)=(112)/(4)`

`r=28`

Using (i), the volume of the sphere is:

`V=(4)/(3)* (22)/(7)* (28)^3`

`V\approx 91989`

Using (ii), the surface area of the sphere is:

`A=4* (22)/(7)* (28)^2`

`A=9856`

Therefore, the surface area of the sphere is 9856 sq. units and the volume of the sphere is 91989 cubic units.