A focused Grade 7 learning session for Cylinder Surface Area and Volume using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving cylinder surface area and volume.
Cylinder Surface Area and Volume is part of Grade 7 Measurement Geometry. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of cylinder surface area and volume using models, equations, and test-style reasoning.
| What to notice | How to use it |
|---|---|
| Numbers, units, labels, diagrams, or graphs | Identify what each part represents before calculating. |
| The relationship in the problem | Connect the model to an equation, comparison, or explanation. |
Use the figures and worked questions in the practice set below as the visual model for this skill.
Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.
For Cylinder Surface Area and Volume, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.
After solving, explain what the answer means in the situation, not just the number you calculated.
I can solve problems involving cylinder surface area and volume.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
A cylinder has a radius of \(3\) m and a height of \(5\) m. What is its volume? Use \(\pi\approx3.14\).
Answer C: \(141.3\) m\(^3\)
Volume of a cylinder \(=\pi r^2 h\approx3.14\times3^2\times5=3.14\times9\times5=141.3\) m\(^3\).
A soup can has a radius of \(2\) inches and a height of \(4\) inches. What is the volume of the can? Use \(\pi\approx3.14\).
Answer B: \(50.24\) in\(^3\)
\(V = \pi r^2 h \approx 3.14 \times 2^2 \times 4 = 3.14 \times 4 \times 4 = 50.24\) in\(^3\).
What is the volume of the cylinder shown? Use \(\pi\approx3.14\).
Answer C: \(75.36\) cm\(^3\)
\(V = \pi r^2 h \approx 3.14 \times 2^2 \times 6 = 3.14 \times 4 \times 6 = 75.36\) cm\(^3\).
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 \(\pi\approx3.14\).
Answer C: \(502.4\) ft\(^3\)
\(V = \pi r^2 h \approx 3.14 \times 4^2 \times 10 = 3.14 \times 16 \times 10 = 502.4\) ft\(^3\).
A cylindrical drum has a radius of \(1.5\) m and a height of \(2\) m. What is its volume? Use \(\pi\approx3.14\).
Answer B: \(14.13\) 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\(^3\).
Which formula gives the volume of the cylinder shown?
Answer B: \(\pi \times 3^2 \times 7\)
The volume formula is \(V = \pi r^2 h\). With \(r=3\) and \(h=7\), this is \(\pi \times 3^2 \times 7\).
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 \(\pi\approx3.14\).
Answer B: \(628\) cm\(^2\)
\(SA = 2\pi r^2 + 2\pi rh = 2(3.14)(5^2) + 2(3.14)(5)(15) = 157 + 471 = 628\) cm\(^2\).
A cylinder has a surface area formula \(SA = 2\pi r^2 + 2\pi rh\). This can also be written as:
Answer A: \(SA = 2\pi r(r + h)\)
Factor out \(2\pi r\) from \(2\pi r^2 + 2\pi rh\) to get \(2\pi r(r + h)\).
Find the lateral surface area (curved side only) of the cylinder shown. Use \(\pi\approx3.14\).
Answer C: \(125.6\) m\(^2\)
Lateral area \(= 2\pi rh \approx 2 \times 3.14 \times 2.5 \times 8 = 125.6\) m\(^2\).
A cylinder has a radius of \(2\) cm and a height of \(9\) cm. What is the total surface area? Use \(\pi\approx3.14\).
Answer C: \(138.16\) 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\(^2\).
A cylindrical can contains a volume of \(376\) cm\(^3\). The radius is \(4\) cm. What is the height of the can? Use \(\pi\approx3.14\).
Answer C: \(7.5\) cm
\(V = \pi r^2 h \Rightarrow 376 = 3.14 \times 16 \times h \Rightarrow h = \frac{376}{50.24} = 7.5\) cm.
