Practice · Grade 7 Geometry
Circle Problems — Practice With Answers
Drill radius, circumference and area in rising difficulty plus a boss question. Each task comes with a hint and full worked solution. Grade 7, free.
Q1 of 7
0 correct
Find the area of the circle (rounded to 2 decimal places).
r = 3, A = πr²
Quick answer
What's the best way to practice circle problems?
Work several problems across all four quantities: always reduce each one to the radius first, then use d = 2r, C = 2πr and A = πr². Mix the directions — sometimes the radius is wanted (r = d/2, r = C/(2π) or r = √(A/π)), sometimes the circumference or area. Always compute with π ≈ 3.14159 and round to two decimal places at the end, exactly like the calculator. Pay special attention to squaring the radius in A = πr².
HowTo
A 4-step solving strategy
This order works for any circle problem — no matter which quantity is given.
- 1Step 1 of 4
Identify the given quantity
Does the problem give the radius, the diameter, the circumference or the area? This diagnosis decides which formula you start from.
- 2Step 2 of 4
Reduce it to the radius
From the diameter: r = d/2. From the circumference: r = C/(2π). From the area: r = √(A/π). If the radius is already given, skip this step.
- 3Step 3 of 4
Substitute for the wanted quantity
With r known, plug into the right formula: d = 2r, C = 2πr or A = πr². For the area, square the radius first, then multiply by π.
- 4Step 4 of 4
Compute with π and round
Use π ≈ 3.14159, never just 3. Round the result to two decimal places and check the unit: circumference in m, area in m².
Examples
Worked examples with full solutions
Four typical grade 7 circle problems. Try each one yourself first, then compare with the solution.
Easy
Find the area for r = 3.
A = πr²
A = π · 3²
A = π · 9
A ≈ 28.27
Check: 9 · 3.14159 ≈ 28.27 ✓
Square first (3² = 9), then multiply by π — don't combine them the other way.
Easy
Find the circumference for r = 6.
C = 2πr
C = 2π · 6
C = 12π
C ≈ 37.70
Check: 12 · 3.14159 ≈ 37.70 ✓
Circumference is a length — nothing is squared here, just multiplied by 2π.
Medium
Find the radius from C = 31.42.
C = 2πr | ÷ 2π
r = C/(2π)
r = 31.42/(2π)
r ≈ 5
Check: 2π · 5 ≈ 31.42 ✓
Divide by 2π, not just by π — otherwise you get twice the radius.
Hard
Boss: Find the radius from A = 50.
A = πr² | ÷ π
r² = A/π = 50/π ≈ 15.92
r = √15.92
r ≈ 3.99
Check: π · 3.99² ≈ 50.0 ✓
Order: divide by π first, then take the root. Taking the root first gives a wrong answer.
Pitfalls
Common mistakes — and how to avoid them
These five traps come up again and again in circle problems.
Confusing radius and diameter
C = 2πr and A = πr² both use the radius. If the diameter is given, halve it first: r = d/2.
Not squaring in the area
A = πr² — the radius is squared. π · r (without the square) is the most common error in circle area.
Using π as just 3
π ≈ 3.14159. Using 3 throws off every result by about 5%.
Wrong order finding the radius from the area
r = √(A/π): divide by π first, then take the root. Taking the root of A first gives a wrong result.
Swapping circumference and area
Circumference is a length (2πr, in m), area is a surface (πr², in m²). Watch the unit of the quantity asked for.
Study
Practice with a plan — three short tips
Always find the radius first
Whatever is given, reduce it to r first. With the radius known, d, C and A become pure substitution. This fixed routine saves time and errors on a test.
Check with the calculator
Solve the problem by hand, then enter the same quantity into the circle calculator and compare each step. That's how you find exactly where a slip happened.
For every wrong answer: ask why
Was it a forgotten square? π taken as 3? Radius instead of diameter? Note the cause — next time you'll spot the mistake instantly.
FAQ
Frequently asked questions about practicing
Glossary
Terms in one sentence
- Radius (r)
- Distance from the center to the edge of the circle — the starting quantity for all formulas.
- Diameter (d)
- Segment through the center, twice as long as the radius: d = 2r.
- Circumference (C)
- Length of the circle line, C = 2πr — a length, given in m.
- Area (A)
- Content of the disk, A = πr² — a surface area, given in m².
- Pi (π)
- Fixed ratio of circumference to diameter, π ≈ 3.14159 — the same for every circle.
- Rearranging
- Solving a formula for the wanted quantity, e.g. A = πr² into r = √(A/π).
- Boss question
- The last and hardest task in a practice set, here the radius from the area.