Question

A cone of a radius and height 21 cm is filled with water. If water from the cone is poured into a cylinder of radius 21 cm, find the height of the cylinder.

Answer 1

Answer:

The volume of water in the cylinder is V = πr^2 * h

V = π * 10^2 * 20 or 2000π

This equals the volume of a cone with radius 5 and unknown height. The volume of a cone is 1/3 * πr^2 * h or 1/3 * 5^2 * h.

V = 25/3 * π * h

Equal these 2 quantities to each other. π cancels out, then multiply both sides of the equation by 3/25 to solve for h. H = 240 cm

Hope that helps!

Answer 2

Answer:

$Height \: of \: the \: water \\ in \: the \: cylinder (H) = 7\:cm$

Step-by-step explanation:

Dimensions of a cone :

radius (r) = 21 cm ,

Height (h) = 21 cm

Dimensions of a cylinder:

Radius (r) = 21 cm,

Height = H cm

According to the problem given,

If water from the cone is poured into a cylinder.

$Volume \: of \: water \: in \: cylinder \\= Volume \: of \: water \: in \: cone$

$\implies \pi r^{2}H = \frac{1}{3} \pi r^{2}h$

$\implies H =\frac{\pi r^{2}h}{3\times \pi r^{2}}\\=\frac{h}{3}\\=\frac{21}{3}\\=7\:cm$

Therefore,

$Height \: of \: the \: water \\ in \: the \: cylinder (H) = 7\:cm$

•••♪