The base of a solid is a circular disk with radius .Find the volume of the solid if parallel cross-sections perpendicular to the base are isosceles right triangles with hypotenuse lying along the
Base.
A) 6
B) 7
C) 16
D) 49
E) None of these

Question

The base of a solid is a circular disk with radius .Find the volume of the solid if parallel cross-sections perpendicular to the base are isosceles right triangles with hypotenuse lying along the
Base. 
A) 6
B) 7
C) 16
D) 49
E) None of these

Quizplus · Accepted Answer

The volume of the solid can be found using the formula for the volume of a cone, $V = \frac{1}{3}\pi r^2 h$, where $r$ is the radius of the base and $h$ is the height. In this case, the solid described is not a standard cone, but we can derive the volume using the given conditions. The cross-sections are isosceles right triangles, meaning their legs are equal, and the hypotenuse lies along the base. If the radius of the base is $r$, then the leg of the triangle (which is also the height of the solid) is $r$, because in an isosceles right triangle, the hypotenuse is $r\sqrt{2}$, and the legs are $r$. The area of each cross-section (triangle) is $\frac{1}{2}bh = \frac{1}{2}r^2$. To find the volume, we integrate this area along the height of the solid, but since the problem does not specify the radius, we cannot calculate a specific numerical value without more information. Therefore, the correct answer is that none of the provided options can be determined as correct without knowing the radius of the base.

The Base of a Solid Is a Circular Disk with Radius