Question

If the no. of sq.cm on the surface
of a sphere is equal to the no. of
cubic cm in its volume, the diametre of the sphere is _________
​

Answer 1

Question :

If the Total Surface Area of square (cm²) is equal to the volume of sphere (cm³). Then Diameter of the sphere is ?

$\rule{150}{0.5}$

Answer :

As we know that T.S.A of sphere is

$\longrightarrow \sf{T.S.A \: = \: 4 \pi r^2 \: \: \: \: \: \: \: ...(1)}$

And, also we know that formula for Volume is :

$\longrightarrow \sf{Volume \: = \: \dfrac{4}{3} \pi r^3 \: \: \: \: \: \: \: ...(2)}$

If, T.S.A is equal to Volume then Equate (1) and (2)

$\longrightarrow \sf{\dfrac{4}{3} \pi r^3 \: = \: 4 \pi r^2} \\ \\ \longrightarrow \sf{\dfrac{r^3}{3} \: = \: r^2} \\ \\ \longrightarrow \sf{r^3 \: = \: r^2 \: \times \: 3} \\ \\ \longrightarrow \sf{r \: = \: 3} \\ \\ \underline{\underline{\sf{Radius \: of \: Sphere \: is \: 3 \: cm}}}$

______________________

As we know that,

$\longrightarrow \sf{Diameter \: = \: 2(Radius)} \\ \\ \longrightarrow \sf{Diameter \: = \: 2(3)} \\ \\ \longrightarrow \sf{Diameter \: = \: 6 \: cm} \\ \\ \underline{\underline{\sf{Diameter \: is \: 6 \: cm}}}$