Volume Of Cylinders

Front

What is the formula for the volume of a cylinder?

Back

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

Front

What does π (pi) represent in the context of a cylinder's volume?

Back

π (pi) is a mathematical constant approximately equal to 3.14, used to calculate the circumference and area of circles.

Front

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

Back

The volume increases by a factor of four, since volume is proportional to the square of the radius (V = π(2r)²h = 4πr²h).

Front

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

Back

Common units include cubic meters (m³), cubic centimeters (cm³), cubic feet (ft³), and cubic yards (yd³).

Front

How do you round a number to the nearest tenth?

Back

Look at the hundredths place; if it's 5 or more, round up the tenths place by one. If it's less than 5, keep the tenths place the same.

Front

Calculate the volume of a cylinder with a radius of 3 units and a height of 5 units. Use π = 3.14.

Back

Volume = πr²h = 3.14 * (3)² * 5 = 141.3 units³.

Front

What is the relationship between the height and volume of a cylinder?

Back

The volume of a cylinder is directly proportional to its height; if the height increases, the volume increases.

Front

If a cylinder has a volume of 1000 cm³ and a height of 10 cm, what is the radius?

Back

Using the formula V = πr²h, rearranging gives r = √(V/(πh)). So, r = √(1000/(3.14*10)) ≈ 5.64 cm.

Front

What is the volume of a cylinder with a diameter of 4 cm and a height of 10 cm? Use π = 3.14.

Back

First, find the radius: r = diameter/2 = 2 cm. Then, Volume = πr²h = 3.14 * (2)² * 10 = 125.6 cm³.

Front

How does changing the height of a cylinder affect its volume if the radius remains constant?

Back

If the radius remains constant, increasing the height will increase the volume proportionally.