# Integral Calculus

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• Sep 30th 2009, 07:08 AM
xwrathbringerx
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? (Worried)
• Sep 30th 2009, 08:58 AM
Grandad
Hello xwrathbringerx
Quote:

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? (Worried)

Imagine the glass to be the solid formed when the line joining $(3,0)$ to $(4,10)$ is rotated about the $y$-axis.

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

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

Can you continue?

Grandad