Question

Find the Radius of a sphere whose volume is 47016 $\pi$cu.cm.

Option :-

=>31.6 cm
=>36 cm
=> 33 cm
=> 22.5 cm
​

Answer 1

★ Concept :-

Here the concept of Volume of Sphere has been used. We see that we need to find the radius of the sphere whose volume is given. So firstly we can assume the radius of sphere as a variable. Then we can apply that into its formula and then equate the formula with the volume given. Thus we can find the answer .

Let's do it !!

_________________________________________

★ Formula Used :-

$\\\;\boxed{\sf{\pink{Volume\;of\;Sphere\;=\;\bf{\dfrac{4}{3}\:\times\:\pi r^{3}}}}}$

_________________________________________

★ Solution :-

Given,

» Volume of the sphere = 47016 π cm³

• Let the radius of the sphere be r

We know that,

$\\\;\sf{\rightarrow\;\;Volume\;of\;Sphere\;=\;\bf{\dfrac{4}{3}\:\times\:\pi r^{3}}}$

By applying values, we get

$\\\;\sf{\Longrightarrow\;\;\dfrac{4}{3}\:\times\:\pi r^{3}\;=\;\bf{47106\:\pi}}$

Now transposing the constant terms from LHS to RHS, we get

$\\\;\sf{\Longrightarrow\;\;r^{3}\;=\;\bf{\dfrac{47106\:\pi}{\bigg(\frac{4}{3}\bigg)\pi}}}$

$\\\;\sf{\Longrightarrow\;\;r^{3}\;=\;\bf{\dfrac{47106\:\pi}{\frac{4}{3}\pi}}}$

$\\\;\sf{\Longrightarrow\;\;r^{3}\;=\;\bf{\dfrac{47106\:\times\:\pi\:\times\:3}{4\:\times\:\pi}}}$

Cancelling π, we get

$\\\;\sf{\Longrightarrow\;\;r^{3}\;=\;\bf{\dfrac{47106\:\times\:3}{4}}}$

$\\\;\sf{\Longrightarrow\;\;r^{3}\;=\;\bf{\dfrac{141048}{4}}}$

$\\\;\sf{\Longrightarrow\;\;r^{3}\;=\;\bf{35262}}$

$\\\;\sf{\Longrightarrow\;\;r\;=\;\bf{\sqrt[3]{35262}}}$

$\\\;\sf{\Longrightarrow\;\;r\;=\;\bf{\sqrt[3]{35262}}}$

$\\\;\sf{\Longrightarrow\;\;r\;=\;\bf{32.79\;\approx\;32.8}}$

And by further rounding off, we get

$\\\;\sf{\Longrightarrow\;\;r\;=\;\bf{32.8\;\approx\;33}}$

$\\\;\bf{\Longrightarrow\;\;r\;=\;\bf{\green{33\;\;cm}}}$

This is the required answer.

→ So the correct option is, (Option) 33 cm

$\\\;\underline{\boxed{\tt{Hence,\;\:radius\;\:of\;\:sphere\;=\;\bf{\purple{33\;\;cm}}}}}$

_________________________________________

★ More to know :-

$\\\;\sf{\leadsto\;\;CSA\;of\;Sphere\;=\;4\pi r^{2}}$

$\\\;\sf{\leadsto\;\;TSA\;of\;Sphere\;=\;4\pi r^{2}}$

$\\\;\sf{\leadsto\;\;CSA\;of\;Hemisphere\;=\;2\pi r^{2}}$

$\\\;\sf{\leadsto\;\;TSA\;of\;Hemisphere\;=\;3\pi r^{2}}$

$\\\;\sf{\leadsto\;\;Volume\;of\;Hemisphere\;=\;\dfrac{2}{3}\pi r^{3}}$

Answer 2

Given,

• Volume of the sphere = 47016 π

To find,

• Radius of sphere = ?

Formula used,

• Volume of the sphere = 4/3πr³

Solution,

Using volume of sphere formula we have to find out the radius of the sphere.

Volume of sphere = 4/3πr³

47016 π = 4/3 × π × r³

r³ = 47016 × π × 3 / 4 × π

r³ = 47016 ×3 / 4 (both pie cancels)

r³ = 141048 / 4

r³ = 35262

r = ³√35262

r = 32.794 cm

Approx = 33 cm

Hence, the radius of the sphere is 33 cm.