1. ## Integral Calculus

A drinking glass has the shape of a truncated cone. If the internal radii of the base and the top are 3 cm and 4 cm respectively and the depth is 10 cm, find by integration, its capacity. If the glass is filled with water to a depth of 5 cm, find the volume of the water.

Could someone please show me how to do this question?

2. Hello xwrathbringerx
Originally Posted by xwrathbringerx
A drinking glass has the shape of a truncated cone. If the internal radii of the base and the top are 3 cm and 4 cm respectively and the depth is 10 cm, find by integration, its capacity. If the glass is filled with water to a depth of 5 cm, find the volume of the water.

Could someone please show me how to do this question?
Imagine the glass to be the solid formed when the line joining $\displaystyle (3,0)$ to $\displaystyle (4,10)$ is rotated about the $\displaystyle y$-axis.

The equation of this line is $\displaystyle y = 10x-30$, and the volume of revolution about the $\displaystyle y$-axis is

$\displaystyle \int_0^{10}\pi x^2dy$

Can you continue?