Question

the surface area of a sphere is of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm find the height and volume of the cone.​

Answer 1

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

Answer 2

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