Question

if the radius of sphere be doubled then the total surface area of new sphere will be how many times of old sphere ​

Answer 1

Answer:

If the radius of the sphere is doubled, then the total surface area of the new sphere will be 4 times that of the old sphere.

Step-by-step-explanation:

We have given that the radius of a sphere is doubled.

We have to find how many times the total surface area of the sphere will be of old sphere.

Now,

Let,

$\displaystyle{\bullet\:\sf\:r}$ be the radius of the old sphere.

$\displaystyle{\bullet\:\sf\:TSA_{old\:sphere}}$ be the total surface area of the old sphere.

$\displaystyle{\bullet\:\sf\:2r}$ be the radius of the new sphere.

$\displaystyle{\bullet\:\sf\:TSA_{new\:sphere}}$ be the total surface area of the new sphere.

Now, we know that,

$\displaystyle{\pink{\sf\:Total\:surface\:area\:of\:sphere\:=\:4\:\pi\:r^2}}$

$\displaystyle{\implies\sf\:TSA_{old\:sphere}\:=\:4\:\pi\:r^2\:\:\:-\:-\:(\:1\:)}$

Now,

$\displaystyle{\sf\:TSA_{new\:sphere}\:=\:4\:\pi\:(\:2r\:)^2}$

$\displaystyle{\implies\sf\:TSA_{new\:sphere}\:=\:4\:\pi\:4\:r^2\:\:\:\:-\:-\:(\:2\:)}$

Now, comparing equations ( 1 ) & ( 2 ), we get,

$\displaystyle{\sf\:\cancel{4}\:\cancel{\pi}\:\cancel{r^2}\:=\:\cancel{4}\:\cancel{\pi}\:4\:\cancel{r^2}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:TSA_{old\:sphere}\:=\:4\:TSA_{new\:sphere}}}}}$

∴ If the radius of the sphere is doubled, then the total surface area of the new sphere will be 4 times that of the old sphere.