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Volumes Help (1 Viewer)

the-derivative

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Hey guys,

Just a volumes question - I'd appreciate it if you guys could help me (I can't get volumes into my head:

3. The base of a solid is a circle x^2 + y^2 = a^2. Each section of the solid by a plane perpendicular to the x-axis is a square. Find the volume of the solid.
Also find the volume of the solid when instead of the square, each section is a right angles isosceles triangle with its right angle above of the plane, a right angles isosceles triangle with its hypotenuse not on the base and an equilateral triangle.

Thanks heaps guys/
 

Trebla

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The side of the square is 2y, so its area is 4y²
δV = 4y²δx
= 4(a² - x²)δx
V = 4∫-aa(a² - x²)dx
Find the integral and this gives the volume. A similar procedure applies with the triangles...
 

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