Question

a cone of radius 5 cm is filled with water if the water poured in a cylinder of radius 10 cm the height of water rises to centimetre find the height of the cone

Answer 1

Mark as brainliest

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:

h = 24

Explanation:

Given:

Radius of cone = 5cm

Radius of cylinder = 10cm

To Find:

find the height of the cone.

procedure

Let's assume the height of the cylinder to be x.

Volume of the Cone :

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: Volume \: of \: the \: Cone : \: \dfrac{1}{3} \times \dfrac{22}{7} \times {r}^{2} \times h {cm}^{3}$

When it is poured the rises is 2cm.

Volume of the cylinder =

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: volume \: of \: the \: water = \dfrac{22}{7} \times 10 \times 10 \times 2 {cm}^{2}$

$volume \: of \: the \: water = \dfrac{22}{7} \times 100 \times 2 {cm}^{2}$

$volume \: of \: the \: water = \dfrac{22}{7} \times 200 {cm}^{2}$

We know that,

Volume of cone = Volume of water

$\implies \sf \: \: \dfrac{22}{7} \times5 \times 5 \times h= \dfrac{22}{7} \times 200 {cm}^{2} {cm}^{3}$

$\dfrac{550}{21}h = \dfrac{4400}{7}$

Multiplying both sides by 21/550.

$\bigg(\dfrac{21}{550} \bigg)\dfrac{550}{21}h = \bigg(\dfrac{21}{550} \bigg)\dfrac{21}{550}$

h = 24

h= 24