The surface area of a sphere of radius 5cm is five times the area of the curved surface of a cone of radius 4cm. Find the height and volume of the cone (pi = 22/7)

Let R be the radius of the sphere.

Suppose the radius of cone be *r* and *h* respectively.

Surface area of the sphere = 4πR^{2} = 4π (5 cm)^{2} = 100π cm^{2}

Curved surface area of cone = *πrl* =* π* × 4 cm × *l *= 4*πl*

Given, Surface area of the sphere = 5 × Curved surface area of the cone

∴ 100*π* cm^{2} = 5 × 4*π l* cm

⇒ 100*π* cm^{2} = 20*πl* cm

⇒ *l* = 5 cm

Slant height of the cone,

∴ (4 cm)^{2} + *h* ^{2} = (5 cm)^{2}

⇒ *h* ^{2} = 25 cm^{2} – 16 cm^{2}

⇒ *h* ^{2} = 9 cm^{2}

⇒ *h* = 3 cm

Height of the cone, *h* = 3 cm

∴ Volume of the cone