8-1: Volume of Cylinders

Front

What is the formula to find the volume of a cylinder?

Back

V = πr²h, where V is the volume, r is the radius, and h is the height.

Front

What is the volume of a cylinder with a height of 10 cm and a radius of 9 cm? Show work.

Back

V = π(9 cm)²(10 cm) = π(81 cm²)(10 cm) = 810π cm³ ≈ 2544.7 cm³.

Front

What is the definition of a radius in a circle?

Back

A radius is a line segment from the center of the circle to any point on the circle.

Front

What is the definition of a diameter in a circle?

Back

A diameter is a line segment that passes through the center of the circle and has its endpoints on the circle.

Front

If a cylinder has a volume of 300π cm³ and a height of 12 cm, what is the radius? Show work.

Back

V = πr²h; 300π = πr²(12); r² = 25; r = 5 cm.

Front

What is the relationship between the radius and diameter of a circle?

Back

The diameter is twice the length of the radius: Diameter = 2 × Radius.

Front

How do you calculate the volume of a cylinder?

Back

Multiply the area of the base (circle) by the height: V = πr²h.

Front

What is the area of the base of a cylinder with a radius of 4 cm?

Back

Area = πr² = π(4 cm)² = 16π cm².

Front

What units are used to measure volume?

Back

Common units for volume include cubic centimeters (cm³), liters (L), and cubic meters (m³).

Front

If the radius of a cylinder is doubled, how does the volume change?

Back

The volume increases by a factor of four, since V = π(2r)²h = 4πr²h.