Question

a sphere of radius r has the same volume as that of a cone with a circular base radius r . Find the height of the cone​

Answer 1

Answer:4/r

Step-by-step explanation:

volume of sphere = 4/3πr³

volume of cone = 1/3πr²h

⇒4/3πr³ = 1/3πr²h

rh = 4

h = 4/r(ans)

hope it helps you!!!!!

if it is wrong,forgive me.

Answer 2

The height of the cone is $h=4r$.

Step-by-step explanation:

Given : A sphere of radius r has the same volume as that of a cone with a circular base radius r.

To Find : The height of the cone​ ?

Solution :

A sphere of radius r.

The volume of the sphere is $V_s=\frac{4}{3}\pi r^3$

A cone with a circular base radius r.

Let the height be h.

The volume of the cone is $V_c=\frac{1}{3}\pi r^2 h$

According to question,

Volume of the sphere = Volume of cone

$\frac{4}{3}\pi r^3=\frac{1}{3}\pi r^2 h$

$4r=h$

Therefore, the height of the cone is $h=4r$

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