Question

If the radius of a sphere is trippled then what is the ratio of their volumes?

Answer 1

Question:-

If the radius of a sphere is trippled then what is the ratio of their volumes?

Required Answer:-

Given Condition:-

• The radius of a sphere is tripled

To Find:-

• The ratio of their volumes

♡Solution:-

Let the original radius be r

As we know that :-

Volume of a sphere:-

$\boxed{ \sf{ \blue{ \bold{V} = \frac{4}{3} \pi \: {r}^{3} }}}$

If the radius is tripled then the new radius = 3r

Hence, the new volume becomes:-

$\sf{ \bold{{V}_{new} }= \frac{4}{3} \pi \times (3r) {}^{3} }$

$\sf{ \bold{{V}_{new} }= \frac{4}{3} \pi \times 27 {r}^{3} }$

Then, the ratio of the volumes:-

$\sf{ Ratio \: of \: the \: volumes} = \: \sf{ \large{ \frac{\frac{4}{3} \pi \: {r}^{3} }{ \frac{4}{3} \pi \times 27 {r}^{3} } } }$

$\sf{ \implies{{ Ratio \: of \: the \: volumes} = \: \sf{ \large{ \frac{1}{27} }}}}$

$\sf{ \implies{{ Ratio \: of \: the \: volumes} = \: \sf{ \large{ \orange{1 \ratio{27}}}}}}$

Therefore,the ratio of their volumes is 1:27

Answer 2

✰ Your Question ☟

• If the radius of a sphere is trippled then what is the ratio of their volumes?

✰ Required Answer ☟

✯ Given ☛ Radius of sphere ➪ Trippled.

✯ To Find ☛ Ratio of their volumes

✠ So, lets start solving,

$\\ ❍  \underline{ \tt \: Let, \: original \: radius \: be \: \boxed{\bf r \: _{(radius)}.}}$

$❒ \: \: \bf \underline {As \: we \: know \: that,}$

$❍ \tt \: \underline {The \: original \: volume \: of \: a \: spehere \: \bf : \implies \: {\color{purple}\frac{4}{3} \pi r {}^{3}} }$

.°. New Radius,

$\\ ✧ \: \boldsymbol {\underline{According \: to \: the \: question,}}$

$\qquad \bull \: \underline{ \tt \: Radius \: of \: the \:sphere \: is \: trippled.}$

Then,

$\\ ❏ \: \bf \: \underline{New \: volume} \: : \implies \: \tt\frac{4}{3} \pi(3r) {}^{3} \\ \: \: \: \: \: \: \: \: \: \qquad \qquad \: \bf \qquad : \implies \: \frac{4}{3} \pi(27 r {}^{3} )$

$\therefore \: \bf \underline {Ratio} \: : \implies \: \tt\frac{ \cancel{\frac{4}{3} \pi} \cancel{ r {}^{3}} }{ \cancel{\frac{4}{3} \pi}( 27 \cancel{r {}^{3}}) } \: \: ➠ \: ✰ \: \: \underline{ \boxed{ \: \frak{\color{purple}{\frac{1}{27} }}} }\: \: ✰$

$\underline{ \boldsymbol{❃\:\:Hence,} \: \tt \: the \: ratio \: of \: their \: volume \: is \bf\: \color{purple}1:27}.$

✯ Hope it helps u ✯