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?
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Answer 1

Answer:

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

Step-by-step explanation:

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

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

Answer 2

Step-by-step explanation:

We have,

→ Volume of cone = Volume of sphere .

$</p><p>\begin{lgathered}\sf \implies \frac{1}{ \cancel3} \cancel\pi \cancel{{r}^{2}} h = \frac{4}{ \cancel3} \cancel \pi {r}^{ \cancel3} . \\ \\ \sf \implies h = 4r. \\ \\ \sf \implies h = 2d. \\ \\ \sf \implies \frac{1}{2} = \frac{d}{h} . \\ \\ \huge \green{ { \tt \therefore d : h = 1 : 2.}}\end{lgathered} </p><p> \:$