Question

The surface area of a sphere of radius 5cmis five times the area ot the CSA of cone of radius 4 cm. Find the i) height ;ii) the volume of the cone .

Answer 1

According to question,
surface area of sphere = 5 × curved surface area of cone.
→4πr² = 5×πrl
→4×5×5 = 5× 4× l
→100 = 20 l
→l = 100/20
so, l = 5cm
then, height of cone = √(l²-r²)
→h = √(5²-4²)
→h = √25-16
→h = √9
so,h = 3cm
Then, volume of cone = 1/3πr²h
= 1/3×22/7×4×4×3
= 22×4×4/7
= 352/7
=50.28cm³