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The radius of a sphere is equal to the radius of a cone and the volume of the sphere is equal to the volume of the cone. Find the curved surface area of the sphere when the height of the cone is 28 m. (Take π = 22/7)

The radius of a sphere is equal to the radius of a cone and the volume of the sphere is equal to the volume of the cone. Find the curved surface area of the sphere when the height of the cone is 28 m. (Take π = 22/7) Correct Answer 616 m<sup>2</sup>

Given:

Radius of a sphere =  Radius of a cone

Volume of the sphere = Volume of the cone

Height of cone = 28 m

Formula used:

(1) Volume of a sphere = (4/3)πr3

(2) Volume of a cone = (1/3)πr2h

(3) Curved surface area of a sphere = 4πr2

where, r = radius and h = height

Calculation:

Let the radius of the sphere be x cm.

Then, Volume of sphere = Volume of cone

⇒ (4/3)π(x)3 = (1/3)π(x)2 × 28 cm

⇒ x = 28/4

⇒ x = 7 m

Now, Curved surface area of the sphere = 4πr2

⇒ 4 × (22/7) × 72 

⇒ 616 m2

∴ The curved surface area of the sphere is 616 m2.

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