A focused Grade 7 learning session for Area of a Circle using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving area of a circle.
Area of a Circle 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 area of a circle 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 Area of a Circle, 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 area of a circle.
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 circle has a radius of \(4\) centimeters. What is its area? Use \(\pi\approx3.14\).
Answer D: \(50.24\) cm\(^2\)
\(A = \pi r^2 = 3.14 \times 4^2 = 3.14 \times 16 = 50.24\) cm\(^2\).
A circle has a diameter of \(10\) feet. What is its radius?
Answer A: \(5\) feet
Radius is half the diameter: \(r = \frac{d}{2} = \frac{10}{2} = 5\) feet.
Which formula should you use to find the area of the circle above? Use \(\pi\approx3.14\).
Answer B: \(A = \pi r^2\)
The area of a circle uses the formula \(A=\pi r^2\). The formula \(2\pi r\) is for circumference.
A circle has a radius of \(3\) inches. What is its area? Use \(\pi\approx3.14\).
Answer C: \(28.26\) in\(^2\)
\(A = \pi r^2 = 3.14 \times 3^2 = 3.14 \times 9 = 28.26\) in\(^2\).
A circle has a diameter of \(8\) meters. What is its area? Use \(\pi\approx3.14\).
Answer B: \(50.24\) m\(^2\)
First find \(r = \frac{d}{2} = 4\) m. Then \(A = 3.14 \times 4^2 = 3.14 \times 16 = 50.24\) m\(^2\).
A circle has a radius of \(7\) centimeters. What is its area? Use \(\pi\approx\frac{22}{7}\).
Answer C: \(154\) cm\(^2\)
\(A = \pi r^2 = \frac{22}{7} \times 7^2 = \frac{22}{7} \times 49 = 22 \times 7 = 154\) cm\(^2\).
A circular rug has a radius of \(2.5\) meters. What is the approximate area of the rug? Use \(\pi\approx3.14\).
Answer C: \(19.625\) m\(^2\)
\(A = 3.14 \times (2.5)^2 = 3.14 \times 6.25 = 19.625\) m\(^2\).
What is the area of this circle? Use \(\pi\approx3.14\).
Answer C: \(78.5\) ft\(^2\)
\(A = \pi r^2 = 3.14 \times 5^2 = 3.14 \times 25 = 78.5\) ft\(^2\).
A circular pool has a radius of \(9\) feet. What is the area of the pool's surface? Use \(\pi\approx3.14\).
Answer C: \(254.34\) ft\(^2\)
\(A = \pi r^2 = 3.14 \times 9^2 = 3.14 \times 81 = 254.34\) ft\(^2\).
A semicircle (half circle) has a radius of \(4\) inches. What is its area? Use \(\pi\approx3.14\).
Answer B: \(25.12\) in\(^2\)
Area of full circle: \(A = \pi r^2 = 3.14 \times 16 = 50.24\) in\(^2\). Semicircle: \(\frac{50.24}{2} = 25.12\) in\(^2\).
A quarter circle has a radius of \(8\) centimeters. What is its area? Use \(\pi\approx3.14\).
Answer C: \(50.24\) cm\(^2\)
Area of full circle: \(A = 3.14 \times 8^2 = 3.14 \times 64 = 200.96\) cm\(^2\). Quarter: \(\frac{200.96}{4} = 50.24\) cm\(^2\).
