Question

A small plastic vessel has the shape of a truncated cone as shown. Find the volume of the cup

Answer 1

To determine the volume of the cone, we use the diagram to the right. We are given that the height of the complete cone is 17.5cm. Notice that the volume of the truncated cone is the volume of the whole cone minus the volume of the smaller cone.

Now, recall that the volume of a cone is given by the following formula:

`V=(1)/(3)\pi r^2h,`

where h is the height of the cone, and r is its radius.

The volume of the whole cone is:

`V_t=(1)/(3)\pi(6.4cm)^2(17.5cm),`

the volume of the small cone is:

`V_s=(1)/(3)\pi(4.8cm)^2(7.5cm).`

Therefore, the volume of the truncated cone is:

`(1)/(3)\pi(6.4cm)^2(17.5cm)-(1)/(3)\pi(4.8cm)^2(7.5cm)=(1)/(3)\pi *544cm^3=(544)/(3)\pi cm^3\approx570cm^3.`

Answer:

`570mililiters.`