Question

using a clay student made a right circular cone of 48 cm and baseradius 12 cm. another student reshapes in the form of a sphere . find the radius of the sphere

Answer 1

Answer :

Given : Height of cone = 48 cm
And
Radius of cone = 12 cm

We know Volume of cone = $\frac{\pi r^{2}h}{3}$ = $\frac{{\displaystyle \frac{22}{7}}\times 12\times 12\times 48}{3}$

And as another student reshaped this cone into sphere . Then volume of this sphere is same as volume of cone .

We know volume of sphere = $\frac{4\pi r^3}{3}$ = $\frac{{\displaystyle 4\times \frac{22}{7}\times r^3}}{3}$
Then
$\Rightarrow \frac{{\displaystyle 4\times \frac{22}{7}\times r^3}}{3}$ = $\frac{{\displaystyle \frac{22}{7}}\times 12\times 12\times 48}{3}$

$\Rightarrow$ 4r ³ = 12 $\times$ 12 $\times$ 48

$\Rightarrow$ r ³ = 12 $\times$ 12 $\times$ 12

$\Rightarrow$r = 12
So,
Radius of sphere = 12 cm ( Ans )