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.

Question

asked Sep 28, 2022 71.5k views

1 Answer

Rajni · Answer 1 · 2022-10-03T16:16:29+0000

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.