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 the water rises 2 centimetre find the height of the cone

Answer 1

vol.cone =vol.cylindrer
1/3 (pi )r2h= (pi)r2h
25×h/3=100×2
h=24

Answer 2

AnswEr:

Let the height of the cone be h cm. Then,

$\mathfrak\red{Volume\:of\:the\:cone}$

$= \sf \dfrac{1}{3} \times \dfrac{22}{7} \times 5 \times 5 \times h \: {cm}^{3}$

When the water in the cone is poured in a cylinder of radius 10cm, the height of the water rises to 2 cm.

$\therefore$ Volume of the water = Volume of a cylinder of radius 10 cm and height 2 cm.

$\implies$ Volume of water = $\sf\dfrac{22}{7}\times\:10\times\:10\times\:2\:cm^3$

But, Volume of the cone = Volume of the water

= $\sf \dfrac{1}{3} \times \dfrac{22}{7} \times 5 \times 5 \times h \: {cm}^{3}$

= $\sf\dfrac{22}{7}\times\:10\times\:10\times\:2$

$\implies$ h = 24 cm

Hence, the height of the cone is 24 cm.

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