Question

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

Answer 1

Aɴsᴡᴇʀ

we have,

• height of cone, h = 25cm
• radius of cone, r = 6cm

we know that,

$\boxed{ \bold{volume \: of \: cone = \frac{1}{3} \pi {r}^{2}h } }$

here, let the volume of cone be V

$\bold{\implies V = \frac{1}{3} \pi {r}^{2} h} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ \implies \:V = \frac{1}{ \cancel{3}} \times \frac{22}{7} \times \cancel{ 6 }\times 6 \times 25 } \\ \\ \bold{\implies V = \frac{22 \times2 \times 6 \times 25}{7} } \: \: \: \: \: \: \: \: \: \\ \\ \implies\boxed{ \red{ \bold{ V = \frac{6600}{7}{cm}^{3} }}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

_________________________

and we know that,

$\boxed{ \bold{volume \: of \: sphere = \frac{4}{3} \pi {r}^{3} }}$

here, let the volume of sphere be v

Since cone made up of modelling clay is reshaped into sphere, so in this case volume remains constant.

Hence, volume of cone = volume of sphere

• let the radius of sphere be R

$\bold{ \implies v = \frac{6600}{7}{cm}^{3} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\\ \\ \bold{ \implies \frac{6600}{7} = \frac{4}{3} \pi {R}^{ 3} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ \implies \frac{6600}{ \cancel{7}} = \frac{4}{3} \times \frac{22}{ \cancel{7}} \times {R}^{3} } \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ \implies R^{3} = \frac{ \cancel{6600} \times 3}{ \cancel{4} \times 22 } } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ \implies R^{3} = \frac{ \cancel{1650} \times 3}{ \cancel{22}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ \implies{R}^{3} = 75 \times 3 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{\implies {R}^{3} = 225 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \boxed{ \pink{\bold{R = \sqrt[3]{225}cm \: \: or \: \: 6.08cm}}}$

so, radius of sphere is 3√225cm or 6.08cm