Question

A cone and a sphere have equal radii and equal volume. what is the ratio of the diameter of the sphere to the height of a cone.

Answer 1

Volume Of Cone÷Volume Of Sphere=4/3pie r^3/1/3pie r^2h
1=4r^3/r^2h
1=2d/h
d/h=1/2
Ratio=1:2

Answer 2

Answer :-

→ d : h = 1 : 2 .

Step-by-step explanation :-

Given :-

→ Radius of cone = Radius of sphere .

→ Volume of cone = Volume of sphere .

To find :-

→Ratio of the diameter of the sphere to the height of the cone .

Solution :-

We have,

→ Volume of cone = Volume of sphere .

$\begin{lgathered}\sf \implies \frac{1}{ \cancel3} \cancel\pi \cancel{{r}^{2}} h = \frac{4}{ \cancel3} \cancel \pi {r}^{ \cancel3} . \\ \\ \sf \implies h = 4r. \\ \\ \sf \implies h = 2d. \\ \\ \sf \implies \frac{1}{2} = \frac{d}{h} . \\ \\ \huge \pink{ \boxed{ \tt \therefore d : h = 1 : 2.}}\end{lgathered}$

Hence, it is solved .