Posted by **Macy** on Thursday, December 1, 2011 at 11:52am.

Let R be the region bounded by the x-axis, x = 5 and the curve

y = x. This region is rotated around the x-axis. Find the volume of the resulting

solid. (Note: R is a triangular region. The resulting solid has a simple shape.

You may ask me if you are highly unsure about what the solid "looks like.")

- Calculus -
**Steve**, Thursday, December 1, 2011 at 12:46pm
geometrically, the solid is a cone of height=5, radius=5

v = 125/3 pi

Analytically,

v = Integral(pi * y^2 dx)[0,5]

= Integral(pi * x^2 dx)[0,5]

= pi/3 x^3 [0,5]

= 125/3 pi

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