Question

The height  of a conical vessel is 3.5 cm. If its capacity is 3.3 litres of milk. Find its diameter of its base.

Answer 1

The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as

Volume of cone = `1/3 pi r^2 h`

It is given that the height of the cone is ‘h’ = 3.5 cm and that the volume of the cone is 3.3 liters

We know that,

1 liter = 1000 cubic centimeter

Hence, the volume of the cone in cubic centimeter is ` 3300  cm^3`. 

We can now find the radius of base ‘r’ by using the formula for the volume of a cone, while using  `pi = 22/7`

`r^2 = (3("Volume of the cone"))/(pih)` 

= `((3)(3300)(7))/((22)(3.5))`

`r^2` = 900

r = 30

Hence the radius of the base of the cone with given dimensions is ‘r’ = 30 cm.

The diameter of base is twice the radius of the base.

Hence the diameter of the base of the cone is  60 cm