Question

The surface area of sphere of radius 5cm is five times the area of CSA of a cone of radius 5 cm. Then find the volume of cone.

Answer 1

Hi.

Here is your answer---

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Given---
Radius of the Sphere(r) = 5 cm.
Radius of the cone(r) = 5 cm.

According to the Questions,

   C.S.A of the Sphere = 5 × C.S.A of the Cone
                       4 π r² = 5 ×π × r × l 
                       4 × 5 × 5 = 5 × l
                                     l = 20 cm.

Now,
 Radius of the cone(r)= 5 cm.
 Slant Height(l)= 20 cm.

Using the Pythagoras Theorem,

   l² = r² + h²
  h² = 400 - 25
  h = √325
 h = 18.02

For volume,
   Volume of the Cone = (1/3)π r² h
                                    = (1/3)(22/7) 5 × 5 × 18.02
                                    =  472.16 cm³.

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Hope it helps.

Have a nice day.