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.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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.

Tags

CCSS.HSG.GMD.A.1

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.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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.

Tags

CCSS.5.MD.A.1