Question

If radius and hieight of solid right circular cylinder, solidnight circular cone, solid sphere are equal, the ratio of their volumes is​

Answer 1

we have already given in the question that

r=h

volume of solid right circular cylinder=$\pi$$r^{2}$h

volume of solid right circular cone   =$\frac{1}{3} \pi$$r^{2}$h

volume of solid sphere                       =$\frac{4}{3}$$\pi$$r^{3}$h

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

solving we get

h:$\frac{1}{3}$ h :$\frac{4}{3}$h

1 :$\frac{1}{3}$ : $\frac{4}{3}$

1:4:3

hence the ratio of there volume is=1:4:3

Answer 2

Given:

If radius and hieight of solid right circular cylinder, solidnight circular cone, solid sphere are equal, the ratio of their volumes is​

Solution:

Know that,

Volume of the right circular cylinder$\[ = \pi {r^2}h\]$

Volume of the right circular cone$\[ = \frac{2}{3}\pi {r^2}h\]$

Volume of the sphere$\[ = \frac{3}{3}\pi {r^3}\]$

where, $r$ is the radius and $h$ is the height,

Find the ratio of their volumes,

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

Put, $h=r$

$\[\begin{array}{l} = \pi {r^2} \times r\frac{1}{3}\pi {r^2} \times r:\frac{4}{3}\pi {r^3}\\ = 1:\frac{1}{3}:\frac{4}{3}\\ = 3:1:4\end{array}\]$

Hence, the required ratio is $3:1:4$.