Question

The diameter of a sphere is 21 cm. The radius of the base of a solid cone is same as the radius of the sphere. If the volumes of the two solids are equal, find the total surface area of the cone.​

Answer 1

Step-by-step explanation:

9th

Maths

Surface Areas and Volumes

Surface Area of Spheres

The volume of a cone is equ...

MATHS

The volume of a cone is equal to that of a sphere. If the diameter of the base of cone is equal to the diameter of the sphere, what is the ratio of the height of the cone to the diameter of the sphere

A

2:1

B

1:2

C

3:1

D

4:1

EASY

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ANSWER

Let R be a radius of a sphere, h and r are height and radius of cone respectively.

Given: Diameter of base of cone= Diameter of sphere

d=D⇒ r=R

Now volumes are equal,

 ∴31πr2h=34πR3

Cancelling 3,π,r&R

∴h=4R

⇒h=42D

⇒h=2D

⇒Dh=2

Thus, h:D=2:1