Question

An inverted cone of height 10 centimetre and base radius 6.4 centimetre contains water to a depth of 5,measured from the vertex.calculate the volume of water in the cone.

Answer 1

volume = 1/3 pi r^2 h 

where r is the radius of the base and h is the height. 

Volume=1/3 x 3.14 x 4 x 15 =3.14 x 20 =62.8 cm^3 

By similar triangle, 

r / h = a / b , a=radius at the water level and b= height from the water level to bottom. 

4 / 15 = a / 10 

=> a = 10 x 4 / 15 

=> a = 40 / 15 = 5 x 8 / 5 x 3 = 8/3 cm 

Now, volume of the water 

= 1/3 x pi x a^2 x b 

=1/3 x 3.14 x (8/3)^2 x 10 

=(31.4 / 3) x (8/3)^2 

=74.4296 cm^3..........cm^3 means cubic cm.