Question

5. A solid has a circle of radius r as its base. All sections of the solid perpendicular to the diameter along the x-axis are isosceles right angled triangles. Find the volume of the solid.(Hint: you have to distinguish two cases). 2

Answer 1

Answer:

 $\frac{16r^3}{3}$

Step-by-step explanation:

In this cross sections problem, we can integrate from -r to +r (so that the integral covers the entire base of the solid).

$\int\limits^r_a {2(x^2+r^2 )} \, dx$

The formatting for the integral did not let me put -r on the lower bound, so i replaced it with a, just know that a represents -r here.

Evaluating the integral gives use that it is equal to;

$\frac{16r^3}{3}$

Caution: this answer may not meet your needs, but this is the answer I have come up with with the given information.

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