Geometry 12.2 Volume of Pyramids

Front

What is the formula for the volume of a pyramid?

Back

The volume V of a pyramid is given by the formula V = (1/3) * B * h, where B is the area of the base and h is the height.

Front

What does the term 'base area' refer to in the context of pyramids?

Back

The base area refers to the surface area of the base shape of the pyramid, which can be a triangle, square, or any polygon.

Front

If a pyramid has a square base with a side length of 4 units and a height of 3 units, what is its volume?

Back

The volume is V = (1/3) * (4 * 4) * 3 = 16 cubic units.

Front

How does the height of a pyramid affect its volume?

Back

The height of a pyramid directly affects its volume; increasing the height while keeping the base area constant will increase the volume.

Front

What is the relationship between the volume of a pyramid and a prism with the same base and height?

Back

The volume of a pyramid is one-third the volume of a prism with the same base area and height.

Front

What is the volume of a pyramid with a triangular base that has an area of 10 square units and a height of 6 units?

Back

The volume is V = (1/3) * 10 * 6 = 20 cubic units.

Front

What is the significance of the factor 1/3 in the volume formula for pyramids?

Back

The factor 1/3 accounts for the fact that a pyramid occupies one-third the volume of a prism with the same base and height.

Front

If the base area of a pyramid is doubled, how does that affect the volume?

Back

If the base area is doubled, the volume of the pyramid also doubles, assuming the height remains constant.

Front

What is the volume of a pyramid with a rectangular base measuring 5 units by 3 units and a height of 4 units?

Back

The volume is V = (1/3) * (5 * 3) * 4 = 20 cubic units.

Front

How do you find the area of a triangular base for a pyramid?

Back

The area A of a triangular base can be found using the formula A = (1/2) * base * height of the triangle.