Question

A cone of height 25cm and radius of base 6cm is made up of modelling clay. A child reshapes it in the form of a sphere, the radius of the sphere​

Answer 1

Given{

Heightofcone=25cm

Radiusofcone=6cm

Given :-

A cone of height is 25 cm and radius of the base is 6 cm is made up of modelling clay.

A child reshapes it in the form of a sphere.

To Find :-

What is the radius of the sphere.

Solution :-

Given :

Height = 25 cm

Radius = 6 cm

First, we have to find the volume of cone,

We know that,

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

Volumeofcone=

3

1

πr

2

h

According to the question by using the formula we get,

⇒ \dfrac{1}{3} {\pi} \times {(6)}^{2} \times 25

3

1

π×(6)

2

×25

⇒ \dfrac{1}{3} {\pi} \times 36 \times 25

3

1

π×36×25

➠ 300 {\pi}300π cm³

Now,

Let, the radius of the sphere be r

We know that,

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

Volumeofsphere=

3

4

πr

3

Now, we know that,

✶ Volume of sphere = Volume of cone ✶

According to the question by using the formula we get,

↦ \dfrac{4}{3}{\pi}{r}^{3} = 300{\pi}

3

4

πr

3

=300π

↦ \dfrac{4}{3}{r}^{3} = 300

3

4

r

3

=300

↦ {r}^{3} = \dfrac{300 \times 3}{4}r

3

=

4

300×3

↦ {r}^{3} = 75 \times 3r

3

=75×3

↦ {r}^{3} = 225r

3

=225

↦ \sqrt[3]{{r}^{3}} = \sqrt[3]{225}

3

r

3

=

3

225

➥ r = 6.082 cm

\therefore∴ The radius of the sphere is 6.082 cm