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 ______.

पर्याय

• 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 `1/3 pir^2 h`.

So, `1/3 pir^2 h = 1/3 pi (2.1)^2 xx 8.4`

Now, volume of sphere = `4/3 pir_1^3`

According to the question,

`4/3 pir_1^3 = 1/3 pi (2.1)^2 xx 8.4`

`4r_1^3 = (2.1)^2 xx 8.4`

`r_1^3 = ((2.1)^2 xx 8.4)/4`

`r_1^3 = (2.1)^2 xx 2.1`

`r_1^3 = (2.1)^3`

r₁ = 2.1

Hence, the radius of the sphere is 2.1 cm.