Question

if the volume of the sphere is numerically equal to its surface area,then find the diameter of the sphere​

Answer 1

Step-by-step explanation:

According to the question,

Volume of sphere = Surface area of sphere

4/3 πr^3 = 4πr^2

r^2*2/3 = r^2

(Here 4 π r^2 will get cancelled (common in both))

therefore, r = 3

2r = d

2(3) = d

6 = d

therefore, diameter of the spere is 6.

verification:

4/3 π r^3 = 4 π r^2

4/3 π 3^3 = 4π 3^2

4 π 9 = 4π 9

36 π = 36π

Thus , d= 6 units.