Understanding Cylinder Geometry

What is the formula for the surface area of a cylinder?

• Surface Area = πr² + h

• Surface Area = 2πr + 2πrh²

• Surface Area = 4πr² + 2πrh

• Surface Area = 2πr² + 2πrh

How do you calculate the volume of a cylinder?

• V = 2πrh

• V = 4/3πr³

• V = πr² + h

• V = πr²h

If the radius of a cylinder is 3 cm and the height is 5 cm, what is its volume?

• 30 cm³

• 141.3 cm³

• 60 cm³

• 100 cm³

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

• 351.68 cm²

• 300 cm²

• 400 cm²

• 250 cm²

Explain the difference between the lateral surface area and the total surface area of a cylinder.

• The total surface area is always larger than the lateral surface area by a fixed amount.

• The lateral surface area is calculated using the diameter, while the total surface area uses the radius.

• The lateral surface area includes the areas of the two bases, while the total surface area is just the curved surface.

• The lateral surface area is the area of the curved surface, while the total surface area includes the lateral area plus the areas of the two bases.

If a cylinder has a volume of 150 cm³ and a height of 5 cm, what is its radius?

• 2.5 cm

• 5.5 cm

• 3.09 cm

• 4.0 cm

How does the surface area of a cylinder change if the radius is doubled?

• The surface area remains the same.

• The surface area of the cylinder increases by a factor of 4.

• The surface area decreases by a factor of 2.

• The surface area increases by a factor of 3.

What units are used for measuring the surface area and volume of a cylinder?

• Surface area: square units; Volume: cubic units.

• Surface area: cubic units; Volume: square units.

• Surface area: linear units; Volume: square units.

• Surface area: square centimeters; Volume: square meters.

If the height of a cylinder is halved, how does that affect its volume?

• The volume is tripled.

• The volume is doubled.

• The volume is halved.

• The volume remains the same.

Provide a real-world example where the volume of a cylinder is important.

• Determining the height of a cylinder based on its diameter.

• Estimating the weight of a solid cylinder.

• Calculating the surface area of a cylinder.

• Designing a water tank to hold a specific volume of water.