Volume of Cylinder

Front

What is the formula for the volume of a cylinder?

Back

The volume V of a cylinder is given by the formula V = πr²h, where r is the radius of the base and h is the height.

Front

How do you calculate the volume of a cylinder with a radius of 5 cm and a height of 10 cm?

Back

Using the formula V = πr²h, V = π(5 cm)²(10 cm) = 250π cm³, which is approximately 785.4 cm³.

Front

What is the relationship between diameter and radius in a cylinder?

Back

The diameter d of a cylinder is twice the radius r, so d = 2r.

Front

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

Back

If the radius is doubled, the volume increases by a factor of four, since volume is proportional to the square of the radius (V ∝ r²).

Front

What is the volume of a cylinder with a height of 7 cm and a base radius of 3 cm?

Back

Using the formula V = πr²h, V = π(3 cm)²(7 cm) = 63π cm³, which is approximately 197.9 cm³.

Front

What units are used to measure the volume of a cylinder?

Back

Volume is typically measured in cubic units, such as cubic centimeters (cm³), liters (L), or cubic meters (m³).

Front

What is the significance of π (pi) in the volume formula of a cylinder?

Back

π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter, and it is essential in calculating the area of the circular base of the cylinder.

Front

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

Back

To convert from cubic centimeters to liters, divide the volume in cm³ by 1000, since 1 liter = 1000 cm³.

Front

What is the volume of a cylinder with a height of 15 cm and a base radius of 4 cm?

Back

Using the formula V = πr²h, V = π(4 cm)²(15 cm) = 240π cm³, which is approximately 753.98 cm³.

Front

What is the effect of increasing the height of a cylinder on its volume?

Back

Increasing the height of a cylinder while keeping the base radius constant will increase the volume linearly, as volume is directly proportional to height (V ∝ h).