Volume of Pyramids, Cones, Cylinders, and Spheres

Front

What is the formula for the volume of a pyramid?

Back

Volume = (1/3) × Base Area × Height

Front

What is the formula for the volume of a cone?

Back

Volume = (1/3) × π × r² × h

Front

What is the formula for the volume of a cylinder?

Back

Volume = π × r² × h

Front

What is the formula for the volume of a sphere?

Back

Volume = (4/3) × π × r³

Front

How do you find the volume of a cone with a height of 30 in. and a diameter of 20 in.?

Back

First, find the radius (r = diameter/2 = 10 in.). Then use the formula: Volume = (1/3) × π × (10 in.)² × 30 in. = 3,142 in³.

Front

What is the volume of a cylinder with a radius of 5 cm and a height of 10 cm?

Back

Volume = π × (5 cm)² × 10 cm = 250π cm³ ≈ 785 cm³.

Front

What is the volume of a sphere with a radius of 3 m?

Back

Volume = (4/3) × π × (3 m)³ = 36π m³ ≈ 113.1 m³.

Front

What is the volume of a pyramid with a base area of 20 m² and a height of 9 m?

Back

Volume = (1/3) × 20 m² × 9 m = 60 m³.

Front

What is the relationship between the volume of a cone and a cylinder with the same base and height?

Back

The volume of a cone is one-third the volume of a cylinder with the same base and height.

Front

If a cylinder has a volume of 1,000 cm³ and a height of 10 cm, what is the radius?

Back

Volume = π × r² × h. Rearranging gives r = √(Volume / (π × h)). So, r = √(1,000 cm³ / (π × 10 cm)) ≈ 5.64 cm.