Circumference and Area of a Circle Worksheet - Math Monks - Free Printable

Explanation:
We are given 8 circles. For each, we need to find the circumference (C) and area (A) using:

- Circumference: $ C = 2\pi r $
- Area: $ A = \pi r^2 $
- Use $ \pi = 3.14 $

Important: Some diagrams show the radius, some show the diameter.

Recall:
- Radius ($ r $) is from center to edge.
- Diameter ($ d $) is across the circle through the center.
- So if diameter is given, radius = $ d \div 2 $.

Let’s go one by one:

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1. Radius = 40 ft
- $ C = 2 \times 3.14 \times 40 = 6.28 \times 40 = 251.2 $ ft
- $ A = 3.14 \times 40^2 = 3.14 \times 1600 = 5024 $ ft²

2. Diameter = 56 cm → radius = $ 56 \div 2 = 28 $ cm
- $ C = 2 \times 3.14 \times 28 = 6.28 \times 28 = 175.84 $ cm
- $ A = 3.14 \times 28^2 = 3.14 \times 784 = 2461.76 $ cm²

3. Radius = 62 in
- $ C = 2 \times 3.14 \times 62 = 6.28 \times 62 = 389.36 $ in
- $ A = 3.14 \times 62^2 = 3.14 \times 3844 = 12070.16 $ in²

4. Radius = 12 cm
- $ C = 2 \times 3.14 \times 12 = 6.28 \times 12 = 75.36 $ cm
- $ A = 3.14 \times 12^2 = 3.14 \times 144 = 452.16 $ cm²

5. Diameter = 102 mm → radius = $ 102 \div 2 = 51 $ mm
- $ C = 2 \times 3.14 \times 51 = 6.28 \times 51 = 320.28 $ mm
- $ A = 3.14 \times 51^2 = 3.14 \times 2601 = 8167.14 $ mm²

6. Radius = 15.5 ft
- $ C = 2 \times 3.14 \times 15.5 = 6.28 \times 15.5 = 97.34 $ ft
- $ A = 3.14 \times (15.5)^2 = 3.14 \times 240.25 = 754.385 $ ft²
(Round to 2 decimals: 754.39 ft² — but since others used 2 decimals, let’s keep 2: 754.39)

Wait — check multiplication:
$ 15.5^2 = 240.25 $
$ 3.14 \times 240.25 $:
$ 3 \times 240.25 = 720.75 $
$ 0.14 \times 240.25 = 33.635 $
Sum = $ 720.75 + 33.635 = 754.385 $ → yes, 754.39 ft²

But many earlier answers were exact without rounding extra digits — let's keep two decimal places consistently.

7. Diameter = 30.5 m → radius = $ 30.5 \div 2 = 15.25 $ m
- $ C = 2 \times 3.14 \times 15.25 = 6.28 \times 15.25 $
Compute:
$ 6 \times 15.25 = 91.5 $
$ 0.28 \times 15.25 = 4.27 $
Total = $ 95.77 $ m
(Or directly: $ 6.28 \times 15.25 = (628 \times 1525)/10000 = 957700/10000 = 95.77 $) ✔
- $ A = 3.14 \times (15.25)^2 $
First, $ 15.25^2 = (15 + 0.25)^2 = 225 + 2×15×0.25 + 0.0625 = 225 + 7.5 + 0.0625 = 232.5625 $
Then $ 3.14 \times 232.5625 $:
Break it:
$ 3 \times 232.5625 = 697.6875 $
$ 0.14 \times 232.5625 = 32.55875 $
Sum = $ 697.6875 + 32.55875 = 730.24625 $ → round to 730.25 m²

8. Radius = 3.5 km
- $ C = 2 \times 3.14 \times 3.5 = 6.28 \times 3.5 = 21.98 $ km
- $ A = 3.14 \times (3.5)^2 = 3.14 \times 12.25 = $
$ 3 \times 12.25 = 36.75 $
$ 0.14 \times 12.25 = 1.715 $
Sum = $ 38.465 $ → round to 38.47 km²

Let me double-check all calculations for accuracy:

1. r=40:
C = 2×3.14×40 = 251.2 ✔
A = 3.14×1600 = 5024 ✔

2. d=56 → r=28:
C = 2×3.14×28 = 175.84 ✔
A = 3.14×784 = let’s compute: 3×784=2352, 0.14×784=109.76 → total 2461.76 ✔

3. r=62:
C = 2×3.14×62 = 6.28×62: 6×62=372, 0.28×62=17.36 → 389.36 ✔
A = 3.14×3844: 3×3844=11532, 0.14×3844=538.16 → 12070.16 ✔

4. r=12:
C = 75.36 ✔
A = 3.14×144 = 452.16 ✔

5. d=102 → r=51:
C = 6.28×51 = 6×51=306, 0.28×51=14.28 → 320.28 ✔
A = 3.14×2601: 3×2601=7803, 0.14×2601=364.14 → 8167.14 ✔

6. r=15.5:
C = 6.28×15.5 = 6×15.5=93, 0.28×15.5=4.34 → 97.34 ✔
A = 3.14×240.25 = 754.385 → 754.39 ✔

7. d=30.5 → r=15.25:
C = 6.28×15.25 = 95.77 ✔
A: 15.25² = 232.5625; ×3.14 = 730.24625 → 730.25 ✔

8. r=3.5:
C = 6.28×3.5 = 21.98 ✔
A = 3.14×12.25 = 38.465 → 38.47 ✔

All correct.

Final Answer:
1. C = 251.2 ft, A = 5024 ft²
2. C = 175.84 cm, A = 2461.76 cm²
3. C = 389.36 in, A = 12070.16 in²
4. C = 75.36 cm, A = 452.16 cm²
5. C = 320.28 mm, A = 8167.14 mm²
6. C = 97.34 ft, A = 754.39 ft²
7. C = 95.77 m, A = 730.25 m²
8. C = 21.98 km, A = 38.47 km²