# Volume of a solid in first quadrant

• Ashford
In summary, to find the volume of the solid with a base in the first quadrant bounded by the curves y=x^2 and y=x, and cross sections perpendicular to the x-axis that are squares, we can use the typical volume element with a base extending from y=x^2 to y=x, having the same height and width of \Delta x. The limits of integration are the values of x where the two curves intersect.
Ashford

## Homework Statement

Find the volume of the solid whose base is the region in the first quadrant bounded by the curves y=x^2 and y=x, and whose cross sections perpendicular to the x-axis are squares.

No idea what to do here

Start by drawing a graph of the region. Then draw a sketch of the solid object.

Ok, I've done that but I still don't know which equation to use and how to set it up.

Your typical volume element has a base that extends from y = x^2 up to y = x, has the same height, and is $\Delta x$ wide. Your limits of integration are the values of x where the two curves intersect.

## What is the "Volume of a solid in first quadrant"?

The volume of a solid in first quadrant is the measure of the amount of space occupied by a three-dimensional object in the first quadrant of a coordinate plane.

## How is the volume of a solid in first quadrant calculated?

The volume of a solid in first quadrant is calculated by finding the product of the base area and the height of the object. The base area is the area of the shape formed by the projection of the object onto the first quadrant, and the height is the distance between the base and the highest point of the object in the first quadrant.

## What is the significance of calculating the volume of a solid in first quadrant?

Calculating the volume of a solid in first quadrant is important in various fields such as architecture, engineering, and physics. It allows for accurate measurements and predictions of the amount of space an object will occupy, which is crucial in designing and constructing structures and analyzing physical properties of materials.

## What types of objects can have a volume in the first quadrant?

Any three-dimensional object that has a base in the first quadrant and extends into the positive x and y directions can have a volume in the first quadrant. This includes shapes such as cubes, prisms, and pyramids.

## Can the volume of a solid in first quadrant be negative?

No, the volume of a solid in first quadrant cannot be negative. Volume is a measure of the amount of space an object occupies, and therefore, cannot be negative as space cannot be "less than nothing".

Replies
4
Views
1K
Replies
2
Views
1K
Replies
3
Views
2K
Replies
1
Views
1K
Replies
3
Views
1K
Replies
1
Views
1K
Replies
8
Views
3K
Replies
2
Views
1K
Replies
8
Views
2K
Replies
4
Views
1K