Volume of cylinders

Front

What is the formula for the volume of a cylinder?

Back

Volume = π × r² × h, where r is the radius and h is the height.

Front

What does 'π' (pi) represent in the volume formula?

Back

π (pi) is a mathematical constant approximately equal to 3.14, representing the ratio of the circumference of a circle to its diameter.

Front

If a cylinder has a radius of 3 inches and a height of 5 inches, what is its volume?

Back

Volume = π × (3 in)² × (5 in) ≈ 141.37 in³.

Front

How does changing the radius of a cylinder affect its volume?

Back

Increasing the radius increases the volume exponentially, as volume is proportional to the square of the radius.

Front

How does changing the height of a cylinder affect its volume?

Back

Increasing the height linearly increases the volume, as volume is directly proportional to height.

Front

What is the volume of a cylinder with a radius of 4 cm and a height of 10 cm?

Back

Volume = π × (4 cm)² × (10 cm) ≈ 502.65 cm³.

Front

What is the relationship between the volume of two cylinders with the same height but different radii?

Back

The volume of a cylinder increases with the square of the radius; thus, a larger radius results in a significantly larger volume.

Front

If a cylinder has a height of 7 inches and a volume of 154 in³, what is its radius?

Back

Using the formula, r = √(Volume / (π × h)) = √(154 in³ / (π × 7 in)) ≈ 2.25 in.

Front

What is the volume of a soda can with a height of 4 inches and a radius of 2 inches?

Back

Volume = π × (2 in)² × (4 in) ≈ 25.13 in³.

Front

How do you convert the volume of a cylinder from cubic inches to cubic centimeters?

Back

Multiply the volume in cubic inches by 16.387 to convert to cubic centimeters.