Introduction

Cylinder Surface Area and Volume is an important Grade 7 math skill because students are moving from simple answers toward explaining how the math works.

In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with cylinder surface area and volume.

What Is Cylinder Surface Area and Volume?

Cylinder Surface Area and Volume means measuring how much flat space a figure covers by using equal-sized square units.

The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.

Understanding Cylinder Surface Area and Volume

Before solving, students should slow down and decide what each number, shape, unit, or label represents.

  • Use square units that cover the figure without gaps or overlaps.
  • Count rows and columns when the unit squares are arranged in an array.
  • Connect repeated addition to multiplication when finding area.
  • Break complex figures into smaller rectangles when that makes the work clearer.

Visual Models

Visual Model 1

Question: What is the volume of the cylinder shown? Use \(\pi\approx3.14\).

Visual Model 1

  • A. \(37.68\) cm\(^3\)
  • B. \(50.24\) cm\(^3\)
  • C. \(75.36\) cm\(^3\)
  • D. \(150.72\) cm\(^3\)

Why it works: \(V = \pi r^2 h \approx 3.14 \times 2^2 \times 6 = 3.14 \times 4 \times 6 = 75.36\) cm\(^3\).

Answer: \(75.36\) cm\(^3\)

Visual Model 2

Question: Which formula gives the volume of the cylinder shown?

Visual Model 2

  • A. \(\pi \times 3 \times 7\)
  • B. \(\pi \times 3^2 \times 7\)
  • C. \(2\pi \times 3 \times 7\)
  • D. \(2\pi \times 3^2 \times 7\)

Why it works: The volume formula is \(V = \pi r^2 h\). With \(r=3\) and \(h=7\), this is \(\pi \times 3^2 \times 7\).

Answer: \(\pi \times 3^2 \times 7\)

Worked Examples

Example 1

Question: Find the lateral surface area (curved side only) of the cylinder shown. Use \(\pi\approx3.14\).

Example 1

  • A. \(39.25\) m\(^2\)
  • B. \(62.8\) m\(^2\)
  • C. \(125.6\) m\(^2\)
  • D. \(188.4\) m\(^2\)
  1. Lateral area \(= 2\pi rh \approx 2 \times 3.14 \times 2.5 \times 8 = 125.6\) m\(^2\).

Answer: \(125.6\) m\(^2\)

Example 2

Question: What is the height of the cylinder if the volume is \(62.8\) in\(^3\) and the radius is \(1\) inch? Use \(\pi\approx3.14\).

Example 2

  • A. \(10\) inches
  • B. \(15\) inches
  • C. \(20\) inches
  • D. \(30\) inches
  1. \(62.8 = 3.14 \times 1^2 \times h \Rightarrow h = \frac{62.8}{3.14} = 20\) inches.

Answer: \(20\) inches

Example 3

Question: Which cylinder has the greater volume?

Example 3

  • A. Cylinder 1
  • B. Cylinder 2
  • C. They are equal
  • D. Cannot be determined
  1. Cylinder 1: \(V = \pi r^2 h = 3.14 \times (1)^2 \times 2 = 3.14 \times 1 \times 2 = 6.28\) units\(^3\).
  2. Cylinder 2: \(V = 3.14 \times (1.5)^2 \times 1.2 = 3.14 \times 2.25 \times 1.2 = 8.478\) units\(^3\).
  3. Cylinder 2 has greater volume.

Answer: Cylinder 2

Real-World Word Problems

Problem 1

Question: A soup can has a radius of \(2\) inches and a height of \(4\) inches. What is the volume of the can? Use \(\pi\approx3.14\).

  • A. \(25.12\) in\(^3\)
  • B. \(50.24\) in\(^3\)
  • C. \(75.36\) in\(^3\)
  • D. \(100.48\) in\(^3\)

Why it works: \(V = \pi r^2 h \approx 3.14 \times 2^2 \times 4 = 3.14 \times 4 \times 4 = 50.24\) in\(^3\).

Answer: \(50.24\) in\(^3\)

Problem 2

Question: A water tank in the shape of a cylinder has a radius of \(4\) feet and a height of \(10\) feet. Find the volume. Use \(\pi\approx3.14\).

  • A. \(125.6\) ft\(^3\)
  • B. \(251.2\) ft\(^3\)
  • C. \(502.4\) ft\(^3\)
  • D. \(1004.8\) ft\(^3\)

Why it works: \(V = \pi r^2 h \approx 3.14 \times 4^2 \times 10 = 3.14 \times 16 \times 10 = 502.4\) ft\(^3\).

Answer: \(502.4\) ft\(^3\)

Common Mistakes

  • Counting only the outside squares instead of all squares inside the figure.
  • Leaving gaps or overlaps when using unit squares.
  • Multiplying side lengths before checking whether the figure is a rectangle.
  • Forgetting to write square units with an area answer.

Strategy Tips

  • Trace the rectangle or figure before counting.
  • Use rows and columns to organize unit squares.
  • Write an equation after the model makes sense.
  • Check whether the answer needs square units.

Practice Questions

Question 1

A cylinder has a radius of \(3\) m and a height of \(5\) m. What is its volume? Use \(\pi\approx3.14\).

  • A. \(47.1\) m\(^3\)
  • B. \(94.2\) m\(^3\)
  • C. \(141.3\) m\(^3\)
  • D. \(235.5\) m\(^3\)

Question 2

A cylindrical drum has a radius of \(1.5\) m and a height of \(2\) m. What is its volume? Use \(\pi\approx3.14\).

  • A. \(9.42\) m\(^3\)
  • B. \(14.13\) m\(^3\)
  • C. \(18.84\) m\(^3\)
  • D. \(37.68\) m\(^3\)

Question 3

A cylindrical pasta jar has a radius of \(5\) cm and a height of \(15\) cm. What is the surface area of the jar (including both circular ends)? Use \(\pi\approx3.14\).

  • A. \(471\) cm\(^2\)
  • B. \(628\) cm\(^2\)
  • C. \(785\) cm\(^2\)
  • D. \(1256\) cm\(^2\)

Question 4

A cylinder has a surface area formula \(SA = 2\pi r^2 + 2\pi rh\). This can also be written as:

  • A. \(SA = 2\pi r(r + h)\)
  • B. \(SA = \pi r(r + h)\)
  • C. \(SA = 2\pi(r^2 + h^2)\)
  • D. \(SA = \pi r(2r + h)\)

Question 5

A cylinder has a radius of \(2\) cm and a height of \(9\) cm. What is the total surface area? Use \(\pi\approx3.14\).

  • A. \(88.36\) cm\(^2\)
  • B. \(112.6\) cm\(^2\)
  • C. \(138.16\) cm\(^2\)
  • D. \(226.08\) cm\(^2\)

Question 6

A cylindrical can contains a volume of \(376\) cm\(^3\). The radius is \(4\) cm. What is the height of the can? Use \(\pi\approx3.14\).

  • A. \(3.75\) cm
  • B. \(5.625\) cm
  • C. \(7.5\) cm
  • D. \(9.375\) cm
Full Answer Explanations Click to show all answers and explanations

Question 1

Answer: \(141.3\) m\(^3\)

Volume of a cylinder \(=\pi r^2 h\approx3.14\times3^2\times5=3.14\times9\times5=141.3\) m\(^3\).

Question 2

Answer: \(14.13\) m\(^3\)

\(V = \pi r^2 h \approx 3.14 \times 1.5^2 \times 2 = 3.14 \times 2.25 \times 2 = 14.13\) m\(^3\).

Question 3

Answer: \(628\) cm\(^2\)

\(SA = 2\pi r^2 + 2\pi rh = 2(3.14)(5^2) + 2(3.14)(5)(15) = 157 + 471 = 628\) cm\(^2\).

Question 4

Answer: \(SA = 2\pi r(r + h)\)

Factor out \(2\pi r\) from \(2\pi r^2 + 2\pi rh\) to get \(2\pi r(r + h)\).

Question 5

Answer: \(138.16\) cm\(^2\)

\(SA = 2\pi r^2 + 2\pi rh \approx 2(3.14)(2^2) + 2(3.14)(2)(9) = 2(3.14)(4) + 113.04 = 25.12 + 113.04 = 138.16\) cm\(^2\).

Question 6

Answer: \(7.5\) cm

\(V = \pi r^2 h \Rightarrow 376 = 3.14 \times 16 \times h \Rightarrow h = \frac{376}{50.24} = 7.5\) cm.

Timed practice quizzes

Related Quizzes

After studying Cylinder Surface Area and Volume, open these two timed quizzes in a new tab for focused extra practice.

Connection to Standards

This lesson supports Grade 7 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.

Summary

Cylinder Surface Area and Volume becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.

GOLDEN RULE

Area means every square unit inside the figure.