Circle area problems worksheet with nine geometry questions requiring calculation of areas of different circular shapes.

Let’s solve each problem one by one. We’ll use the formula for the area of a circle:
Area = π × r², where r is the radius.

We’ll also remember:
- A semicircle is half a circle → divide full area by 2.
- A quarter circle is 1/4 of a full circle → divide by 4.
- For shapes made of multiple parts, add or subtract areas as needed.
- Always round to 2 decimal places at the end.

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Problem 1: Semicircle with diameter 8 cm

Radius = 8 ÷ 2 = 4 cm

Full circle area = π × 4² = π × 16 ≈ 50.2655 cm²
Semicircle = 50.2655 ÷ 2 ≈ 25.13 cm²

✔ Final Answer for #1: 25.13

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Problem 2: Quarter circle with radius 4.7 mm

Area = (π × 4.7²) ÷ 4
First, 4.7² = 22.09
Then, π × 22.09 ≈ 69.398
Divide by 4 → 69.398 ÷ 4 ≈ 17.35 mm²

✔ Final Answer for #2: 17.35

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Problem 3: Circle missing a small slice — but we’re given radius = 11 m

Wait — looking at the shape, it looks like almost a full circle, but actually, from the diagram, it seems like it’s 3/4 of a circle? Let me check again.

Actually, no — in many such worksheets, if it's drawn like Pac-Man with a wedge missing, and only radius is given without angle, sometimes it’s meant to be full circle minus a sector — BUT here, since no angle is given, and it’s labeled just “11 m” as radius, and the shape is mostly filled... wait — let me re-express.

Looking carefully: The blue shape has a straight line across the top right — that suggests it’s 3/4 of a circle. Because a full circle would have no flat edge. This has two radii forming a 90° gap? Actually, visually, it looks like 270° out of 360° — so 3/4.

But let’s confirm: In standard Cazoom Maths problems, when they show a circle with a triangular wedge cut out and label the radius, and the remaining part is colored, it’s often 3/4 circle if the missing part is a right angle.

Assuming that: Area = (3/4) × π × r²
r = 11 m
r² = 121
π × 121 ≈ 380.1327
× 3/4 = 285.0995 → 285.10 m²

But wait — maybe it’s a full circle? No, because there’s a visible缺口 (gap). Since no angle is specified, and this is level 7.G.B.4 (middle school), likely it’s intended to be 3/4 circle.

Alternatively — perhaps it’s a full circle? But the drawing clearly shows a missing sector. Without an angle, we can’t compute exact fraction — unless...

Wait! Looking back at problem 3: The arrow points to the radius, and the shape is a circle with a V-shaped cutout — which typically represents 270 degrees, i.e., 3/4 circle.

I think it’s safe to assume 3/4.

So:

Area = (3/4) × π × 11² = (3/4) × π × 121 = (363/4) × π = 90.75 × π ≈ 90.75 × 3.1416 ≈ 285.099 → 285.10

✔ Final Answer for #3: 285.10

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Problem 4: Two quarter circles making a half circle? Wait — look: two red quarter-circles arranged to form a sort of bowtie. Total height is 16 mm.

Each quarter circle has radius = half of 16 mm? Wait — the vertical dimension is 16 mm, and each quarter circle spans from center to edge — so radius = 16 ÷ 2 = 8 mm

There are two quarter circles → total area = 2 × (1/4) × π × r² = (1/2) × π × 64 = 32π ≈ 100.53 mm²

Wait — let me double-check: Each quarter circle has radius 8 mm? Yes, because the full height from top to bottom is 16 mm, and each quarter circle goes from center to outer edge — so yes, radius = 8 mm.

Two quarter circles = half a circle → area = (1/2) × π × 8² = (1/2) × π × 64 = 32π ≈ 100.53096 → 100.53 mm²

✔ Final Answer for #4: 100.53

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Problem 5: Purple shape — looks like three-quarters of a circle? Or what?

It’s a purple shape with a dashed line down the middle — and labeled 12 cm from center to tip. So radius = 12 cm.

The shape covers 270 degrees? Let’s see: It has three "petals"? No — actually, it looks like a circle divided into four quadrants, and three are shaded? Wait — no, it’s symmetric — actually, it looks like three-quarters of a circle.

Yes — similar to problem 3, but now it’s clearly 3/4 circle.

Area = (3/4) × π × 12² = (3/4) × π × 144 = 108π ≈ 339.292 → 339.29 cm²

✔ Final Answer for #5: 339.29

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Problem 6: Yellow shape — looks like three-quarters of a circle again? Height is 4 m.

Vertical dimension is 4 m — that should be the diameter? Or radius?

Look: The shape extends from top to bottom — and the dashed lines suggest symmetry. If the total height is 4 m, and it’s made of circular arcs, then likely the radius is 2 m? Wait — no.

Actually, in problem 6, the yellow shape has a vertical span of 4 m — and it looks like it’s composed of three quarter-circles? Or perhaps it’s 3/4 of a circle with radius 2 m?

Wait — let’s think differently. The shape resembles a “Pac-Man” rotated, but with three sections. Actually, counting the segments: it has three identical curved parts — each is a quarter circle? And together they make 3/4 of a full circle.

And the distance from top to bottom is 4 m — which would be the diameter of the full circle? Then radius = 2 m.

If radius = 2 m, and area is 3/4 of circle:

Area = (3/4) × π × 2² = (3/4) × π × 4 = 3π ≈ 9.4248 → 9.42 m²

But wait — is the 4 m the diameter or the radius? The arrow spans the entire height of the shape — which for a 3/4 circle oriented this way, the height equals the diameter.

Yes — so radius = 2 m.

✔ Final Answer for #6: 9.42

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Problem 7: Square with side 12 cm, with a white circle inside touching all sides → so circle diameter = 12 cm → radius = 6 cm

Shaded area = area of square - area of circle

Square area = 12 × 12 = 144 cm²
Circle area = π × 6² = 36π ≈ 113.097 cm²
Shaded = 144 - 113.097 ≈ 30.90 cm²

✔ Final Answer for #7: 30.90

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Problem 8: Gray shape — looks like a quarter circle? With height 110 km.

The shape is bounded by two straight lines (forming a right angle) and a curve — so it’s a quarter circle with radius 110 km.

Area = (1/4) × π × 110² = (1/4) × π × 12100 = 3025π ≈ 9503.317 → 9503.32 km²

✔ Final Answer for #8: 9503.32

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Problem 9: Square with diagonal 19 mm, and a white region that is a quarter circle? Wait — let’s analyze.

The gray area is the square minus a white region. The white region is bounded by two sides of the square and a curve — which looks like a quarter circle centered at one corner.

The diagonal of the square is 19 mm. So first, find side length of square.

For a square, diagonal d = s√2 → s = d / √2 = 19 / √2 ≈ 19 / 1.4142 ≈ 13.435 mm

But wait — the white region: it’s a quarter circle whose radius is equal to the side of the square? Because it starts at one corner and curves to the adjacent corners.

So radius r = side of square = s = 19 / √2

But we need area of gray region = area of square - area of quarter circle

Area of square = s² = (19 / √2)² = 361 / 2 = 180.5 mm²

Area of quarter circle = (1/4) × π × r² = (1/4) × π × s² = (1/4) × π × 180.5 ≈ (1/4) × 3.1416 × 180.5 ≈ (0.7854) × 180.5 ≈ 141.7647

Gray area = 180.5 - 141.7647 ≈ 38.7353 → 38.74 mm²

Wait — let me verify:

s = 19 / √2
s² = 361 / 2 = 180.5 — correct.

Quarter circle area = (1/4)πr² = (1/4)πs² = (π/4)*180.5

π/4 ≈ 0.785398
0.785398 × 180.5 ≈ let’s compute:

0.785398 × 180 = 141.37164
0.785398 × 0.5 = 0.392699
Total ≈ 141.764339

Gray area = 180.5 - 141.764339 = 38.735661 → rounded to 2 decimals: 38.74

✔ Final Answer for #9: 38.74

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## Final Answers:

1) 25.13
2) 17.35
3) 285.10
4) 100.53
5) 339.29
6) 9.42
7) 30.90
8) 9503.32
9) 38.74