Question

A cone of height 24cm and radius of base 6cm is made up of modelling clay.child reshapes it in the form sphere .find the radius of the sphere​

Answer 1

Given: Radius & Height of cone is 6 cm and 24 cm respectively.

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

》Let's consider the radius of sphere be R cm.

⠀⠀⠀⠀

$\underline{\boldsymbol{\bigstar\:According\:to\:the\:Question}}$

• A cone is reshaped in the form of sphere.

⠀⠀⠀⠀

Therefore,

⠀⠀⠀⠀

$:\implies\sf Volume\:of\:cone = Volume\:of\:cylinder\\ \\ \\ :\implies\sf \dfrac{1}{3} \times \cancel{\dfrac{22}{7}} \times (6)^2 \times 24 = \dfrac{4}{3} \times \cancel{\dfrac{22}{7}} \times R^3\\ \\ \\ :\implies\sf \dfrac{1}{\cancel{3}} \times 36 \times \cancel{24} = \dfrac{4}{3} \times R^3\\ \\ \\ :\implies\sf 36 \times 8 = \dfrac{4}{3} \times R^3\\ \\ \\ :\implies\sf R^3 = 36 \times \cancel{8} \times \dfrac{3}{\cancel{4}}\\ \\ \\:\implies\sf R^3 = 36 \times 2 \times 3\\ \\ \\:\implies\sf R^3 = 216\\ \\ \\:\implies\sf \sqrt[3]{R^3} = \sqrt[3]{216} \\ \\ \\:\implies{\underline{\boxed{\frak{\purple{R = 6\:cm}}}}}\\\\\\ \therefore\:{\underline{\sf{Radius\:of\:sphere\:formed\:is\: {\textsf{\textbf{6\:cm}}}.}}}$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

$\qquad\qquad\qquad\boxed{\underline{\underline{\bf{\pink{\bigstar \: Formulas\:used\:\bigstar}}}}}$

• $\sf Volume\:of\:cone = \bf{\dfrac{1}{3} \pi r^2 h}$

• $\sf Volume\:of\:sphere = \bf{\dfrac{4}{3} \pi r^3}$

Answer 2

Answer:

Given :-

• A cone of height is 24 cm and radius of base is 6 cm and its is made up of modelling clay and child reshapes it in the form of sphere.

To Find :-

• What is the radius of the sphere.

Formula Used :-

$\sf\boxed{\bold{\small{Volume\: of\: cone\: =\: \dfrac{1}{3}{\pi}{r}^{2}h}}}$

$\sf\boxed{\bold{\small{Volume\: of\: sphere\: =\: \dfrac{4}{3}{\pi}{r}^{3}}}}$

Solution :-

Let, the radius be r cm

First, we have to find the volume of cone,

Given :

• Radius = 6 cm
• Height = 24 cm

According to the question by using the formula we get,

⇒ $\sf Volume\: of\: cone\: =\: \dfrac{1}{3} \times {\pi} \times {(6)}^{2} \times 24$

⇒ $\sf Volume\: of\: cone\: =\: \dfrac{1}{3} \times {\pi} \times 6 \times 6 \times 24$

⇒ $\sf Volume\: of\: cone\: =\: \dfrac{1}{\cancel{3}} \times {\pi} \times {\cancel{864}}$

➦ $\bold{Volume\: of\: cone\: =\: 288{\pi}c{m}^{3}}$

Now, according to the question,

↦ $\sf \dfrac{4}{3}{\cancel{\pi}}{r}^{3} =\: 288{\cancel{\pi}}$

↦ $\sf \dfrac{4}{3} \times {r}^{3} =\: 288$

↦ $\sf {r}^{3} =\: \dfrac{288 \times 3}{4}$

↦ $\sf {r}^{3} =\: \dfrac{\cancel{864}}{\cancel{4}}$

↦ $\sf {r}^{3} =\: 216$

↦ $\sf r =\: \sqrt[3]{216}$

➠ $\sf\bold{\red{r =\: 6\: cm}}$

$\therefore$ The radius of the sphere is 6 cm .