Question

find the total surface area of sphere whose volume is equal to the volume of a cone having radius 12 centimetre and height 6 CM ​

Answer 1

The total surface area of a sphere whose volume is equal to the volume of a cone is 452.57 cm³.

Step-by-step explanation:

Dimensions of the cone:

Radius, r₁ = 12 cm

Height, h = 6 cm

Let the radius of the sphere be “r₂” cm.

It is given that,

Volume of the cone = Volume of the sphere

⇒ $\frac{1}{3}$ * πr₁² h = $\frac{4}{3}$  * πr₂³

⇒ $\frac{1}{3}$ * 12² * 6 = $\frac{4}{3}$ * r₂³

⇒ r₂³ = $\frac{12^2 * 6}{4}$

⇒ r₂ = ∛[6 * 12 * 3]

⇒ r₂ = 6 cm

Thus,  

The total surface area of the sphere is given by,

= 4πr₂²

= 4 * $\frac{22}{7}$ * (6)²

= 452.57 cm²

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