Rectangular Prisms, Pyramids, and Cones

Front

What is the formula for the volume of a rectangular prism?

Back

V = l × w × h, where l is length, w is width, and h is height.

Front

How do you calculate the volume of a pyramid?

Back

V = (1/3) × B × h, where B is the area of the base and h is the height.

Front

What is the formula for the volume of a cone?

Back

V = (1/3) × π × r² × h, where r is the radius of the base and h is the height.

Front

What does the term 'base area' refer to in volume calculations?

Back

The area of the base shape of the solid, used in the volume formula.

Front

If a rectangular pyramid has a base of 10 ft by 5 ft and a height of 12 ft, what is its volume?

Back

V = (1/3) × (10 × 5) × 12 = 200 ft³.

Front

What is the volume of a square pyramid with a base side of 4 m and a height of 6 m?

Back

V = (1/3) × (4 × 4) × 6 = 32 m³.

Front

How do you find the height of a pyramid if you know the volume and base area?

Back

Rearrange the formula: h = (3V) / B.

Front

What is the volume of a cone with a radius of 3 cm and a height of 9 cm?

Back

V = (1/3) × π × (3)² × 9 ≈ 84.8 cm³.

Front

What is the significance of the number 3 in the volume formulas for pyramids and cones?

Back

It represents that the volume is one-third of the product of the base area and height.

Front

If a rectangular prism has dimensions 2 m, 3 m, and 4 m, what is its volume?

Back

V = 2 × 3 × 4 = 24 m³.