Question

a cone of height 24 cm and radius of base 6 cm is made up of modelling clay a child moles it in the form of a sphere find the radius of the sphere

Answer 1

height of the cone =24cm
radius r=6cm
let Its volume Vc
let radius of the sphere =R
let volume of the sphere Vs
then,their volume must be equal
Vs=Vs
4/3piR^3=pir^2h
R^3=3r x r xh/4
R^3=3x6x6x24/4
R=6x root3
R=6x1.732
R=10.40cm (approx).

Answer 2

$\huge{\underline{\underline{\bf{GIVEN:-}}}}$

• Height of the cone = 24 cm
• base radius of cone = 6 cm

$\huge{\underline{\underline{\bf{TO\:FIND:-}}}}$

Find the radius of the sphere = ?

$\huge{\underline{\underline{\bf{FORMULA \:USED:-}}}}$

$\large\underline\mathrm\red{Volume \:of \: cone = \frac{1}{3} π {(r)}^{2} h}$

$\large\underline\mathrm\red{Volume\: of \: Sphere = \frac{4}{3}π{(r)}^{3}}$

$\huge{\underline{\underline{\bf{SOLUTION:-}}}}$

〖Let the radius of sphere be 'r' cm〗

✪$\rm\red{Vol. \:of\: cone = Vol. \:of \:Sphere }$✪ 

☞ On putting the values in formula, we get

$\implies$$\large\rm{\frac{1}{3}π{r}^{2}h = \frac{4}{3}π{(r)}^{3}}$

$\implies$$\rm{\frac{1}{3}π{6}^{2}\times 24 = \frac{4}{3}π{(r)}^{3}}$

$\implies$$\rm{\frac{1}{\cancel{3}}\cancel{π}\times{(6)}^{2}\times 24 = \frac{4}{\cancel{3}}\cancel{π}{(r)}^{3}}$

$\implies$$\rm{6 \times 6 \times 24 = 4 \times {r}^{3}}$

$\implies$$\rm{{(r)}^{3} = \large\frac{6 \times 6 \times \cancel{24}}{\cancel{4}}}$

$\implies$$\rm{{(r)}^{3} = 6 \times 6 \times 6 }$

$\implies$$\rm{r = \sqrt{ 6 \times 6 \times 6 }}$

$\implies$$\large\rm\red{r = 6 \: cm}$

Thus, the radius of sphere is 6 cm

$\large{\underline{\underline{\bf{FINAL\:ANSWER:-}}}}$

$\huge{\boxed{\rm{\red{Radius = 6 \: cm}}}}$