Question

A cone height 240m and radias
of base 6om is made up of
modelling clay A child reshapes within
the form of a sphone find the radius
of sphere?​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Radius\:of\:sphere=60\:m}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Height \: of \: cone = 240 \: m \\ \\ \tt: \implies Radius \: of \: cone = 60 \: m \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Radius \: of \: sphere \: form= ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies Volume \: of \: cone = \frac{1}{3} \pi {r}^{2} h \\ \\ \tt: \implies Volume \: of \: cone = \frac{1}{3} \times \pi \times {60}^{2} \times 240 \\ \\ \tt: \implies Volume \: of \: cone = \frac{1}{3} \times \pi \times 3600 \times240 \\ \\ \green{\tt: \implies Volume \: of \: cone =28800\pi \: {m}^{3}} \\ \\ \bold{As \: according \: to \: question} \\ \tt: \implies Volume \: of \: sphere = Volume \: of \: cone \\ \\ \tt: \implies Volume \: of \: sphere =28800\pi \\ \\ \tt: \implies \frac{4}{3} \pi {r}^{3} = 28800\pi \\ \\ \tt: \implies {r}^{3} = \frac{28800\pi \times 3}{4\pi} \\ \\ \tt: \implies {r}^{3} =21600 \\ \\ \tt: \implies {r} = \sqrt[3]{216000} \\ \\ \green{\tt: \implies {r} =60 \: m}\\\\ \green{\tt\therefore Radius\:of\:sphere\:form\:is\:60\:m}$

Answer 2

$</p><p>\huge{\tt{\pink{Hello!!! }}}$

$</p><p>\huge{\red{\boxed{\boxed{Volume_{Cone} = \frac{1}{3} \pi {r}^2 h }}}}$

[tex] \tt{ \purple{where = > \begin{cases}

r & \text{radius} \\

h & \text{height}

\end{cases}}}[/tex]

Volume Of Cone = Volume Of Sphere

$</p><p>\huge{\blue{\boxed{\boxed{Volume_{Sphere} = 4 \pi {r}^3 }}}}$

Hence ,

$\tt{ \orange{ \frac{1}{3}\pi {r}^{2}h = 4\pi {r}^{3} = > r \: = \: \frac{h}{12} = 20m }}$