Question

A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is ______.

विकल्प

• 4.2 cm

• 2.1 cm

• 2.4 cm

• 1.6 cm

Answer 1

A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is 2.1 cm.

Explanation:

The formula of volume of the cone is ${\displaystyle \frac{1}{3}\pi r^{2}h}$.

So, ${\displaystyle \frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi {\left(2.1\right)}^2\times 8.4}$

Now, volume of sphere = ${\displaystyle \frac{4}{3}\pi r_1^3}$

According to the question,

${\displaystyle \frac{4}{3}\pi r_1^3=\frac{1}{3}\pi {\left(2.1\right)}^2\times 8.4}$

${\displaystyle 4r_1^3={\left(2.1\right)}^2\times 8.4}$

${\displaystyle r_1^3=\frac{{\left(2.1\right)}^2\times 8.4}{4}}$

${\displaystyle r_1^3={\left(2.1\right)}^2\times 2.1}$

${\displaystyle r_1^3={\left(2.1\right)}^3}$

r₁ = 2.1

Hence, the radius of the sphere is 2.1 cm.