Question

If a cone and a sphere have equal radii and equal volumes. What is the ratio of the diameter of the sphere to the height of the cone?

Answer 1

Answer:

The ratio of the diameter of the sphere to the height of the cone is 1 : 2.

Step-by-step explanation:

SOLUTION :  

Let r be the radius of cone and sphere and h be the Height of cone.

Given :  

Radius of cone and sphere = r

Volume of cone = Volume of sphere  

⅓ πr²h = 4/3 πr³

h = 4r

h = 2r × 2

h/2r = 2/1

h/d = 2/1  

[Diameter,d = 2r]

d/h = ½  

Diameter of sphere/ height of a cone = ½

d : h = 1 : 2

Hence, the ratio of  diameter of sphere to height of a cone  is 1 : 2.

HOPE THIS ANSWER WILL HELP YOU….

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 .

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

Hence, it is solved .