Volume of Cylinders

Multiple Choice

Find the volume of a cylinder with a radius of 3 cm and a height of 7 cm. Use the formula $$V = \pi r^2 h$$ .

• $$197.82$$ cm³

• $$395.64$$ cm³

• $$593.46$$ cm³

• $$791.28$$ cm³

Multiple Select

Sheila believes that the two cylinders shown in the diagram below have equal volumes. Is Sheila correct or incorrect? Select ALL that apply.

• Sheila is incorrect. The volumes of both cylinders are not equal.

• Sheila is incorrect. One of the cylinders is tilted.

• Sheila is correct. When two cylinders have the same base areas and the same height, their volumes must be the same.

• Sheila is correct. Both cylinders radii and height are equal, so their volumes are the same.

• Sheila is correct. Using Cavalieri’s Principle and the formula $$v=Bh$$ or $$v=\pi r^2h$$ proves the volumes of the cylinders are equal.

Multiple Select

A series of coins are stacked to represent a right circular cylinder (on the left). The coins are then "slid" to represent a distorted cylinder (on the right). The same number of congruent coins was used in each stack.

Which of the following statements will be TRUE regarding these stacks of coins?

• The volume of both stacks will be the same.

• The area of a cross section parallel to the bases will not be equal due to the distorted nature of the second stack.

• The height of the distorted stack will be slightly larger than that of the straight stack.

• Cavalieri's Principle can be used in this situation to verify that the volumes of the stacks are equal.

Explanation Slide...

To find the volume of a cylinder, use the formula V = πr²h. Substituting r=3 cm and h=7 cm, V = π(3)²(7) = 63π ≈ 197.82 cm³. Therefore, the correct answer is 197.82 cm³.

Multiple Choice

A cylindrical container has a radius of 4 cm and a height of 6 cm. What is its volume? Use the formula $$V = \pi r^2 h$$ .

• $$301.4$$ cm³

• $$603.2$$ cm³

• $$402.4$$ cm³

• $$201.2$$ cm³

Explanation Slide...

To find the volume of a cylinder, use the formula V = πr²h. Substituting r = 4 cm and h = 6 cm, V = π(4²)(6) = 603.2 cm³. Therefore, the correct answer is 603.2 cm³.

Multiple Choice

If the volume of a cylinder is $$706.5$$ cm³ and the radius is 3 cm, what is the height of the cylinder? Use the formula $$V = \pi r^2 h$$ .

• 5 cm

• 10 cm

• 25 cm

• 20 cm

Explanation Slide...

Using the formula V = πr^2h, we can solve for h: h = V / (πr^2) = 706.5 / (π * 3^2) ≈ 25 cm. Therefore, the correct answer is 25 cm.

Multiple Choice

Which of the following is the correct formula to calculate the volume of a cylinder?

• $$V = \pi r h$$

• $$V = \pi r^2 h$$

• $$V = 2\pi r h$$

• $$V = \pi r^2$$

Explanation Slide...

The correct formula to calculate the volume of a cylinder is V = \pi r^2 h, where r is the radius and h is the height of the cylinder.

Multiple Choice

A cylindrical can has a diameter of 10 cm and a height of 12 cm. What is its volume? Use the formula $$V = \pi r^2 h$$ .

• $$942$$ cm³

• $$1884$$ cm³

• $$471$$ cm³

• $$314$$ cm³

Explanation Slide...

The volume of a cylinder is calculated using the formula V = πr^2h. Given diameter = 10 cm, radius = 5 cm. Substituting r = 5 cm and h = 12 cm into the formula gives V = π(5)^2(12) = 942 cm³.

Multiple Choice

Find the volume of a cylinder with a radius of 5 cm and a height of 10 cm. Use the formula $$V = \pi r^2 h$$ .

• $$785.4$$ cm³

• $$1570.8$$ cm³

• $$2356.2$$ cm³

• $$3141.6$$ cm³

Explanation Slide...

To find the volume of a cylinder, use the formula V = πr²h. Substituting r = 5 cm and h = 10 cm, V = π(5)²(10) = 785.4 cm³. Therefore, the correct answer is 785.4 cm³.

Multiple Choice

A cylindrical water tank has a radius of 5 meters and a height of 8 meters. How much water can it hold? Use the formula $$V = \pi r^2 h$$ .

• $$628$$ m³

• $$1256$$ m³

• $$1884$$ m³

• $$2512$$ m³

Explanation Slide...

The formula for the volume of a cylinder is V = πr^2h. Substituting r = 5m and h = 8m, we get V = π(5^2)(8) = 1256 m³. Therefore, the tank can hold 1256 cubic meters of water.

Dropdown

The cylinder has a height of ​

Select answer

and a radius of ​ ​

Select answer

. The shape of the base of the cylinder is a ​

Select answer

Drag and Drop

This shape is a ​

Placeholder

. The formula for this shape is ​

Placeholder

The radius of the shape is ​

Placeholder

and the height is ​

Placeholder

. The volume of this shape is ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

cylinder

Bh

3

10

282.74

cone

sphere

6

350

1/3 Bh

Math Response

Find the volume of the solid. Round to the nearest tenth.

Type answer here

Correct Answer: 37.7

Deg^°

Rad