Question

Find the ratio of the volumes of a come and of a cylinder whose base Diameter and heights are equal. ​

Answer 1

Aim :-

To find the ratio of the volumes of a cone to a cylinder

Given :-

The diameters and heights are equal.

Let the diameter be 2r.Hence radius = 2r/2 = r

Let the height be represented by h.

VOLUME OF A CYLINDER :- πr²h

VOLUME OF A CONE :- ⅓ πr²h

$\dfrac{ \frac{1}{3} \times \pi {r}^{2}h }{\pi {r}^{2}h} = ratio \: of \: the \: volumes$

Cancelling all the common terms,

$= \dfrac{ \frac{1}{3} \times \cancel {\pi {r}^{2}h} }{ \cancel{\pi {r}^{2}h} }$

$= \dfrac{ \dfrac{1}{3} }{1}$$\dfrac{1}{3} \div 1$$= \dfrac{1}{3}$

Hence the ratio of their volumes :- 1 : 3

Some more formulas :-

Volume of a cube = a³

Volume of a cuboid = Length × Breadth × Height

Volume of a sphere = 4/3 × πr³

Volume of a hemisphere = ⅔ × πr³.

Answer 2

Step-by-step explanation:

the volume of cone=

\frac{1}{3} \pi {r}^{2} h31πr2h

volume of cylinder is

\pi {r}^{2}hπr2h

therefore ratio is

1 \: ratio \: 31ratio3

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