# How do you find the volume of the solid with base region bounded by the curve #9x^2+4y^2=36# if cross sections perpendicular to the #x#-axis are isosceles right triangles with hypotenuse on the base?

By signing up, you agree to our Terms of Service and Privacy Policy

To find the volume of the solid with base region bounded by the curve (9x^2 + 4y^2 = 36) if cross sections perpendicular to the x-axis are isosceles right triangles with hypotenuse on the base, you can use the method of integration. First, find the equation for the curve in terms of y. Then, integrate the area of a single cross section over the given range of x-values. This involves integrating the area of an isosceles right triangle, which is (\frac{1}{2} \times \text{base} \times \text{height}). The base of each triangle corresponds to the width of the cross section, and the height corresponds to the length of one of the legs. Finally, integrate the expression for the area of each cross section with respect to x over the interval that covers the entire base region. This integral will give you the volume of the solid.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How would you find the volume of the tetrahedron T bounded by the coordinate planes and the plane 3x+4y+z=10?
- The base of a solid is the region in the first quadrant bounded by the line x+2y=4 and the coordinate axes, what is the volume of the solid if every cross section perpendicular to the x-axis is a semicircle?
- How do you find the area bounded by #x=8+2y-y^2#, the y axis, y=-1, and y=3?
- How do you find the area bounded by #y=x#, #y=1/x^2# the x axis, and x=3?
- How do you use the Disk method to set up the integral to find the volume of the solid generated by revolving about the y-axis the region bounded by the graphs of and the line #y = x#, and #y = x^3# between x = 0 and x = 1?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7