Volumes

**xwrathbringerx** · May 3rd 2010, 06:28 AM

Hi

For this question:

The base of a particular solid is the region bounded by the parabola y^2=4x between its vertex (0,0) and its latus rectum. Find the volume of the solid if every cross-section perpendicular to the x-axis is an equilateral triangle with one side in the base of the solid.

I do not get the solution attached at the circled bit. Could someone please show me how that line was obtained from the above lines?

**TKHunny** · May 3rd 2010, 08:34 AM

What is the area of an equilateral triangle, given the length of one side? Break out your geometry and make it clear. Chop it up into two equal right triangles if you must.

**xwrathbringerx** · May 3rd 2010, 10:28 AM

i've got the area and the value of s in the solutions but when i sub s into the equation of the area, i only get x * sqrt(3)?

**TKHunny** · May 3rd 2010, 12:20 PM

Originally Posted by xwrathbringerx

i've got the area

Keep trying...

Area of Equilateral Triangle:

$y = 2\cdot \sqrt{x}$

$Base = 2\cdot y = 2\cdot (2\cdot \sqrt{x}) = 4\cdot \sqrt{x}$

$Height = \sqrt{3}\cdot y = \sqrt{3}\cdot (2\cdot \sqrt{x})$

$Area = \frac{1}{2}\cdot (4\cdot \sqrt{x}) \cdot (\sqrt{3}\cdot 2\cdot \sqrt{x}) = 4\cdot \sqrt{3} \cdot x$

If I had to guess, I would guess that you are missing that extra '2' on the Base. The value 'y' is only half the base, but that is a good value for calculating the height.

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