# The base of a certain solid is the triangle with vertices at (-8,4), (4,4), and the origin. Cross-sections perpendicular to the y-axis are squares. How do you find the volume of the solid?

Please see below.

Here is a picture (graph) of the base (in blue) with a thin slice taken perpendicular to the

The thinkness of this representative slice is

The line on the right contains

The line on the left contains

The side of the square built on the representative slice is

So,

The volume of the representative slice is

The values of

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

To find the volume of the solid, we need to determine the area of the base and then integrate the area to find the volume.

The base of the solid is a triangle with vertices at (-8,4), (4,4), and the origin. This triangle has a base of 12 units (from (-8,4) to (4,4)) and a height of 4 units (from the base to the origin along the y-axis). Therefore, the area of the base triangle is:

Area = 1/2 * base * height = 1/2 * 12 * 4 = 24 square units.

Since the cross-sections perpendicular to the y-axis are squares, the area of each square cross-section will be equal to the area of the base triangle.

To find the volume of the solid, we integrate the area of the base over the range of y-values for which the solid exists. In this case, the solid exists from y = 0 to y = 4 (the height of the base triangle).

Therefore, the volume of the solid is:

Volume = ∫[0,4] 24 dy = 24y ∣[0,4] = 24(4) - 24(0) = 96 cubic units.

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.

- The base of a certain solid is the triangle with vertices at (-8,4), (4,4), and the origin. Cross-sections perpendicular to the y-axis are squares. How do you find the volume of the solid?
- How do you find the volume of the solid bounded by the coordinate planes and the plane #8x + 6y + z = 6#?
- How do you find the area under the graph of #f(x)=cos(x)# on the interval #[-pi/2,pi/2]# ?
- How do you find the area between #f(x)=x^2-4x+3# and #g(x)=-x^2+2x+3#?
- A rectangular piece canvass with dimensions 10m by 6m is used to make a pool.Equal sizes squares are to be cut from each corner and remaining will folded up around some plastic tubing.what is the dimension of the pool so the water volume is maximum?

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