Question

A cone of height 24cm and radius of the base 6cm is made up of moulding clay. A child reshaped it in the form of sphere, find the volume of sphere.(π=3.14)​

Answer 1

EXPLANATION.

Height of a cone = 24cm.

Radius of the base of the cone = 6cm.

A child reshape and form sphere.

As we know that,

⇒ Volume of cone = 1/3πr²h.

⇒ Volume of sphere = 4/3πr³.

⇒ Volume of cone = Volume of sphere.

⇒ 1/3πr²h = 4/3πr³.

Put the values in the equation, we get.

⇒ πr²h = 4πr³.

⇒ r²h = 4r³.

⇒ 6 x 6 x 24 = 4 x r³.

⇒ 6 x 6 x 6 = r³

⇒ (6)³ = r³.

⇒ r = 6cm.

⇒ Volume of sphere = 4/3πr³.

⇒ 4/3 x 3.14 x 6 x 6 x 6.

⇒ 2712.96/3 = 904.32cm³.

Volume of sphere = 904.32cm³.

Answer 2

Answer:

Given :-

• A cone of height is 24 cm and radius of the base is 6 cm is made up of moulding clay.
• A child reshaped it in the form of sphere. (π = 3.14)

To Find :-

• What is the volume of sphere.

Formula Used :-

$\clubsuit$ Volume of Cone :

$\longmapsto \sf\boxed{\bold{\pink{Volume\: of\: Cone =\: \dfrac{1}{3}{\pi}{r}^{2}h}}}$

$\clubsuit$ Volume of Sphere :

$\longmapsto \sf\boxed{\bold{\pink{Volume\: of\: Sphere =\: \dfrac{4}{3}{\pi}{r}^{3}}}}$

Solution :-

First, we have to find the volume of the cone :

Given :

• Height = 24 cm
• Radius = 6 cm

According to the question by using the formula we get,

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

$\implies \sf Volume\: of\: Cone =\: \dfrac{1}{3}{\pi} \times 36 \times 24$

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

$\implies \sf\bold{\green{Volume\: of\: Cone =\: 288{\pi}}}$

Now, we have to find the radius :

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

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

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

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

$\implies \sf {r}^{3} =\: 216$

$\implies \sf r =\: \sqrt[3]{216}$

$\implies \sf\bold{\purple{r =\: 6\: cm}}$

Now, we have to find the volume of sphere :

Given :

• Radius = 6 cm
• π = 3.14

According to the question by using the formula we get,

$\leadsto \sf Volume\: of\: Sphere =\: \dfrac{4}{3} \times 3.14 \times {(6)}^{3}$

$\leadsto \sf Volume\: of\: Sphere =\: \dfrac{4}{3} \times 3.14 \times 216$

$\leadsto \sf Volume\: of\: Sphere =\: \dfrac{4}{\cancel{3}} \times {\cancel{678.24}}$

$\leadsto \sf Volume\: of\: Sphere =\: 4 \times 226.08$

$\leadsto\sf\bold{\red{Volume\: of\: Sphere =\: 904.32\: {cm}^{3}}}$

$\therefore$ The volume of sphere is 904.32 cm³.