Question

The surface area of a sphere of radius 5 cm is five times the curved surface of a one of radis 4 cm. Find the height and the volume of cone (take π =22/7
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Answer 1

Answer:

50.29 cm³

Step-by-step explanation:

Radius of the sphere (r1) = 5 cm

Radius of the base of cone (r2) = 4 cm

Let r сm be the height of the cone.

Surface area of sphere = 4πr2 ⇒ 4π(5)2 = 100π cm2

Curved surface area of cone = πrl = 4πl cm2

where l is the slant height of the cone.

According to the statement,

100π = 5(4πl) ⇒ l = 5 cm

Now, h2 = l2 - r2 = 52 – 42 = 32 ⇒ h = 3 cm

∴ Volume of cone = 1/3πr2h = 1/3 x 22/7 x 42 x 3

= 352/7 cm3 = 50.29 cm3 (Approximately)

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