Question

Q5)If the volume of a sphere is numerically equal to its surface area,
then find the diameter of the sphere.

Answer 1

Answer:

If the volume of a sphere is numerically equal to its surface area,

then the diameter of the sphere is 6 unit.

Step-by-step explanation:

Given: The volume of a sphere is numerically equal to its surface area.

Find: The diameter of the sphere.

Formula:

The volume of a sphere = $\frac{4}{3} \pi r^3$

The surface area of sphere =$4\pi r^2$

As per the given condition

The volume of a sphere = The surface area of a sphere

[tex]\frac{4}{3} \pi r^3 =4\pi r^2\\ \frac{1}{3} r =1\\ r = 3 unit[/tex]

The radius of the sphere = 3 unit

The diameter of the sphere = 2 (r) = 2(3) = 6 unit

So,  the diameter of the sphere is 6 unit.