Exercise: Calculating the volume of a cylinder for 9th graders

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Ngày cập nhật gần nhất: 15/4/2026

In today's 9th-grade Math session, Mytour will compile and share exercises on calculating the volume of a cylinder from the Textbook (TB), Exercise Book (EB), and additional advanced exercises to aid 9th-grade students in practice. Teachers can also refer to create a diverse and useful resource bank.

In the previous article, Mytour shared exercises on calculating the surface area of a cylinder for 9th graders, covering the lateral surface area and total surface area. In this article, we continue to provide 9th-grade students with exercises on calculating the volume of a cylinder.

Exercises on calculating the volume of a cylinder for 9th graders

Attention: - Refer to the formula for calculating the volume of a cylinder to recall this basic knowledge
- The unit of volume is m3, dm3, cm3 .... With many exercises, the question may provide various units, so students need to convert them to a single unit for accurate calculation and completion.

Exercises on calculating the volume of a cylinder for 9th grade in the Textbook

Exercise 5 (page 111 Textbook Math 9 volume 2): Fill in the blanks in the table below with the correct results:

Solution:

For a cylinder with a base radius r and height h:

+ Circumference of the base: C = 2π.r

+ Area of the base: Sb = π.r²

+ Lateral surface area: Sl = 2πrh

+ Volume: V = π.r².h

Exercise 6 (page 111 Textbook Math 9 volume 2): The height of a cylinder equals the radius of its circular base. The lateral surface area of the cylinder is 314 cm2. Calculate the radius of the circular base and the volume of the cylinder (round the result to the second decimal place).

Solution:

Exercise 10 (page 112 Textbook Math 9 volume 2): Calculate:

a) The lateral surface area of a cylinder with a circumference of the circular base is 13cm and a height of 3cm.

b) The volume of a cylinder with a radius of the circular base is 5mm and a height of 8mm.

Solution:

We have: C = 13cm, h = 3cm

The lateral surface area of the cylinder is:

Sl = 2πr.h = C.h = 13.3 = 39 (cm2)

b) Given: r = 5mm, h = 8mm

The volume of the cylinder is:

V = πr².h = π. 52.8 = 200π ≈ 628 (mm3)

Exercise 11 (page 112 Textbook Math 9 volume 2): Completely submerge a small stone statue into a cylindrical glass jar filled with water (h.84). The area of the glass jar's base is 12.8cm2. The water in the jar rises by an additional 8.5mm. Determine the volume of the stone statue.

Solution:

The volume of the stone statue equals the volume of the cylinder with a base area of 12.8cm2 and a height equal to 8.5mm = 0.85cm (As the volume of the statue equals the volume of water displaced). Thus:

V = S.h = 12.8 . 0.85 = 10.88 (cm3)

Exercise 12 (page 112 Textbook Math 9 volume 2): Fill in the blanks in the table below with the correct results:

Solution:

Exercises on calculating the volume of a cylinder for 9th grade in the Exercise Book

Exercise 1 page 163 Exercise Book Math 9 Volume 2: The area and perimeter of a rectangle ABCD (AB > AD) are in the order of 2a2 and 6a. If the rectangle rotates around side AB, it forms a cylinder. Calculate the volume and lateral surface area of this cylinder.

Solution:

Exercise 3 page 163 Exercise Book Math 9 Volume 2: A cylinder has a radius of the circular base of 6cm, and a height of 9cm. Calculate:

a) The lateral surface area of the cylinder

b) The volume of the cylinder

(Take π = 3.142 and round the result to the nearest integer)

Solution:

a) The lateral surface area of the cylinder is:

Sl = 2πr.h = 2.3.142.6.9 ≈ 339 (cm2)

b) The volume of the cylinder is:

V = π.R².h = 3.142.62.9 ≈ 1018 (cm3)

Exercise 6 page 164 Exercise Book Math 9 Volume 2: An object in the shape of a cylinder has a radius of the circular base and its height both equal to 2r (cm). A hole is drilled with a shape like the following cylinder, with both the radius of the base and the depth equal to r (cm). The volume of the remaining object (measured in cm3) is:

A.4πr³B.7πr³ C.8πr³ D.9πr³

Solution:

Exercise 7 page 164 Exercise Book Math 9 Volume 2: The figure below is a piece of cheese cut from a cylindrical cheese block (with dimensions as shown in the drawing). The mass of the cheese piece is:

A.100g B.100πg

C.800g D.800 πg

(The density of cheese is 3g/cm3). Choose the correct result.

Solution:

Volume of the cylindrical cheese block:

V = π .10².8 = 800 π (cm3)

The volume of the cheese piece is 15/360 =1/24 of the volume of the cheese block

The mass of the cheese piece: m = (1/24) .800 π .3 = 100 π (g)

So the volume of the cheese piece is:

800 π. 1/24 = 100 π/3 cm3

The mass of the cheese piece is m = 3. 100 π/3 = 100 π g

Choose option B

Advanced and supplementary exercises on calculating the volume of a cylinder for 9th grade

Exercise 1: Given a cylinder with a height equal to 8a. A plane parallel to the axis and 3am away from the axis cuts the cylinder into a square cross-section. Calculate the lateral surface area and volume of the cylinder.

Solution:

Exercise 2: A glass cylinder is snugly placed into a rigid cardboard box shaped like a rectangular prism with a height of 15cm and a square base of side length 8cm (the height of the cone equals the height of the cylinder, ...). Calculate the radius of the base and the volume of the glass cylinder.

Exercise 3: Calculate the total surface area of a cylinder with a base circumference of 25cm and a height of 5cm.

Problem 4: Calculate the radius and height of a cylinder given that its lateral surface area and volume are both 62.8.

Problem 5: Rotate the rectangle ABCD with AB = 2BC around side AB to obtain cylinder with volume V1. Rotate the same rectangle around side BC to obtain cylinder with volume V2. Compare V1 and V2.

Let's practice solving cylinder volume exercises for 9th grade to handle any related problems confidently during tests and exams.

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