Question

Find the volume of a solid with a triangular base with vertices at (0,0), (3,0), and (0,2) and cross-sections perpendicular to the y-axis are isosceles triangles with height equal to the base?

Answer 1

The volume of the solid with a triangular base can be found using the formula V = Ah, where A is the area of the triangular base and h is the height of the solid. The base of the triangle is 3 units and the height is 2 units. Therefore, the volume is 9 cubic units.

Step-by-step explanation:

To find the volume of the solid with a triangular base, we can use the formula V = Ah, where A is the area of the triangular base and h is the height of the solid.

The base of the triangle is the distance between the points (0,0) and (3,0), which is 3 units. The height of the triangle is the distance between the point (0,0) and (0,2), which is 2 units.

Therefore, the area of the base is (1/2) * base * height = (1/2) * 3 * 2 = 3 square units.

The height of the solid is the same as the height of the isosceles triangles, which is equal to the base length of the triangles. So, the height is also 3 units.

Now, we can plug the values into the volume formula to get V = (3 square units) * (3 units) = 9 cubic units.