Question

The ratio of the radius of sphere A to the radius of sphere B is 3:4. What is the ratio of the area of sphere A to the area of sphere B?

Answer 1

$\sf\large\underline{Given:}$

$\rm{\implies Ratio\: radius\:_{(S_a\::\:S_b)}=3:4}$

$\sf\large\underline{To\: Find:}$

$\rm{\implies Ratio\: area\:_{(S_a\::\:S_b)}=?}$

$\sf\large\underline{Solution:}$

• Simply by applying formula to calculate area of sphere than calculate it's ratio]

$\sf\large\underline{Formula\:used:}$

$\tt{\implies Area\:_{(Sphere)}=4\pi\:r^2}$

$\tt{\implies Sphere\:_{(A)}=Sphere\:_{(B)}}$

$\tt{\implies 4\pi\times\:3^2=4\pi\times\:4^2}$

$\tt{\implies 9:16}$

$\sf\large{Hence,}$

$\rm{\implies Ratio\: area\:_{(S_a\::\:S_b)}=9:16}$

$\rm\purple{\implies Some\:Note\: about\:it}$

A sphere is like a shape of ball. It has three dimensional space in its surface. It is represented in the form of set of points. As we know that we measure the radius of the circle from the centre point. But in three dimensional space.