Question

If the number of square centimeters in the surface area of a sphere is equal to the number of cubic cm in its volume. Find the diameter of the sphere solve this problem

Answer 1

$4\pi {r}^{2} = \frac{4}{3} \pi {r }^{3} \\ {r}^{2} = {r}^{3} \frac{1}{3} \\ 3 = r \\ r = 3cm \\ d = 2r \\ d = 6cm$

Answer 2

The diameter of the sphere is 6 cm

Step-by-step explanation:

Let the radius of sphere be r

So, Surface area of sphere = $4 \pi r^2$

Volume of sphere =$\frac{4}{3} \pi r^3$

We are given that the number of square centimeters in the surface area of a sphere is equal to the number of cubic cm in its volume.

So, $4 \pi r^2=\frac{4}{3} \pi r^3$

$r^2=\frac{1}{3} r^3$

3=r

So, Radius of sphere = 3 cm

Diameter of sphere = 2r =2(3)=6 cm

Hence the diameter of the sphere is 6 cm

#Learn more:

Find volume of a sphere at CSA 144 pi centimeter square?

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