Volume of Pyramids and Cones

Front

What is the formula for the volume of a pyramid?

Back

The volume of a pyramid is given by the formula: V = (1/3) * base area * height.

Front

What is the formula for the volume of a cone?

Back

The volume of a cone is given by the formula: V = (1/3) * π * r² * h, where r is the radius of the base and h is the height.

Front

How do you find the base area of a rectangular pyramid?

Back

The base area of a rectangular pyramid is found by multiplying the length and width of the base: Base Area = length * width.

Front

What is the relationship between the height and volume of a pyramid?

Back

The volume of a pyramid increases with an increase in height, assuming the base area remains constant.

Front

If the height of a cone is doubled, what happens to its volume?

Back

If the height of a cone is doubled, its volume also doubles, assuming the base radius remains constant.

Front

What is the significance of the factor 1/3 in the volume formulas for pyramids and cones?

Back

The factor 1/3 accounts for the fact that pyramids and cones occupy one-third of the space of a prism or cylinder with the same base area and height.

Front

Calculate the volume of a pyramid with a base area of 100 cm² and a height of 30 cm.

Back

V = (1/3) * 100 cm² * 30 cm = 1000 cm³.

Front

Calculate the volume of a cone with a radius of 5 cm and a height of 12 cm.

Back

V = (1/3) * π * (5 cm)² * (12 cm) ≈ 314.16 cm³.

Front

What is the volume of a pyramid with a square base of side 4 m and a height of 9 m?

Back

Base Area = 4 m * 4 m = 16 m²; V = (1/3) * 16 m² * 9 m = 48 m³.

Front

What is the volume of a cone with a diameter of 10 cm and a height of 15 cm?

Back

Radius = 5 cm; V = (1/3) * π * (5 cm)² * (15 cm) ≈ 78.54 cm³.