Perimeter and Area (Area of circle) worksheet - Free Printable

Let’s solve each problem one by one, step by step. We’ll use the formulas:

- Circumference of a circle = 2 × π × radius (or C = 2πr)
- Area of a circle = π × radius² (or A = πr²)
- For ratio problems: if radii are in ratio a:b, then circumferences are also in ratio a:b (since circumference is directly proportional to radius).
- When wire is reshaped, its length stays the same — so perimeter of original shape = circumference of new circle.

We’ll use π ≈ 22/7 for all calculations unless otherwise needed.

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Problem 1:
Radius = 14 cm
Circumference = 2 × (22/7) × 14
= 2 × 22 × 2 = 88 cm

✔ Final Answer for Q1: 88

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Problem 2:
Radius = 10 m
Circumference = 2 × (22/7) × 10
= (440)/7 ≈ 62.857... but let’s keep it exact as fraction or round? Since worksheet likely expects decimal or simplified form.

Wait — actually, 2 × 22/7 × 10 = 440/7 = 62 and 6/7 → but maybe they want decimal? Let’s check context.

Looking at other problems, some have whole numbers. But here, 440 ÷ 7 = 62.857… Hmm. Maybe we should leave as fraction? But answer box has “m” — probably expects decimal.

But wait — perhaps use π = 3.14? The worksheet doesn’t specify. In Indian curriculum (Class 7), often π = 22/7 is used.

So 440/7 = 62.857… but that’s messy. Let me recalculate:

Actually, 2 × 22/7 × 10 = (2×10×22)/7 = 440/7 = 62 6/7 m → but maybe they expect 62.86? Or perhaps I made a mistake?

Wait — no, let’s do it properly:

2 × π × r = 2 × (22/7) × 10 = (440)/7 = 62.857... → but since it's money or measurement, maybe round to 2 decimals? But worksheet doesn't say.

Alternatively, perhaps they accept fractional form? But answer box is blank with unit — likely expects number.

Wait — looking at Problem 3: radius 4 km → 2×22/7×4 = 176/7 ≈ 25.14 — again not nice.

But Problem 1 gave 88 — which is clean because 14 is multiple of 7.

Perhaps for non-multiples, we still compute exactly.

But let’s proceed with fractions or decimals as appropriate.

Actually, in many worksheets, they expect you to use π = 22/7 and write the answer as a mixed number or decimal.

For Q2: 440/7 = 62 6/7 → but maybe write as decimal 62.86? However, let’s see what makes sense.

Wait — perhaps I should use calculator-style precision? But student may not have.

Another thought: maybe the worksheet expects answers using π = 22/7 and simplified.

So for Q2: 2 × 22/7 × 10 = 440/7 = 62 6/7 m → but that’s unusual.

Wait — let me check online or standard practice. Actually, in Class 7 NCERT, they often leave as fraction or use 22/7 and simplify.

But 440/7 cannot be simplified. So perhaps write as 62.86? But let’s hold on.

Actually, let’s look at Problem 5 and 6 — they involve decimals, so maybe decimals are acceptable.

To avoid confusion, I’ll calculate numerically with π = 22/7 and give decimal rounded to two places where needed.

But for consistency, let’s do exact values first.

Actually, rethinking: in such worksheets, if radius is integer and divisible by 7, answer is integer; else, they might expect fractional or decimal.

But let’s proceed with calculation:

Q2: 2 * 22/7 * 10 = 440/7 = 62.857... → approximately 62.86 m? But let’s see the answer format — it says "m", so probably number.

I think for accuracy, I'll use 22/7 and write the exact value, but since it's a fill-in, likely decimal.

Wait — perhaps I can write it as 62.86, but let's confirm with another approach.

No, better to use 22/7 consistently.

Let me calculate all with 22/7 and see.

Q1: 2*22/7*14 = 88 — good.

Q2: 2*22/7*10 = 440/7 = 62 6/7 — but how to write? Perhaps 62.86 if rounded.

But let's look at Q3: 2*22/7*4 = 176/7 = 25 1/7 ≈ 25.14

This is getting messy. Perhaps the worksheet intends for us to use π = 3.14? Let me try that.

If π = 3.14:

Q1: 2*3.14*14 = 6.28*14 = 87.92 — but earlier with 22/7 it was 88, which is cleaner. And 14 is chosen to make 22/7 work nicely.

Similarly, Q8: radius 7cm — area = π*49 = 22/7*49 = 154 — nice number.

So definitely, they intend π = 22/7.

Therefore, for Q2: 440/7 = 62 6/7 — but since it's a box, perhaps write as decimal 62.86? Or maybe they accept fraction.

But in the image, the answer boxes are empty rectangles, so likely expect numerical value.

Perhaps write as 62.86, but let's see the instruction — "solve accurately".

Another idea: perhaps leave as improper fraction? Unlikely.

I recall that in some systems, they write it as mixed number, but here space is small.

Let's move to Q4 which is ratio — easy.

Q4: Ratio of radii 3:2, so ratio of circumferences is also 3:2, since C ∝ r.

So answer is 3:2.

Q5: Wire rectangle 18.7 cm long, 14.3 cm wide. Perimeter = 2*(l+w) = 2*(18.7 + 14.3) = 2*33 = 66 cm.

This becomes circumference of circle: 2πr = 66

So 2*(22/7)*r = 66

(44/7)r = 66

r = 66 * 7 / 44 = (66/44)*7 = (3/2)*7 = 21/2 = 10.5 cm

Nice! So r = 10.5 cm

Q6: Equilateral triangle side 6.6 cm, so perimeter = 3*6.6 = 19.8 cm

This becomes circumference of circle: 2πr = 19.8

2*(22/7)*r = 19.8

(44/7)r = 19.8

r = 19.8 * 7 / 44

Calculate: 19.8 / 44 = 198/440 = 99/220 = 9/20? Let's compute numerically.

19.8 * 7 = 138.6

138.6 / 44 = ?

44 * 3 = 132, 138.6 - 132 = 6.6, so 3 + 6.6/44 = 3 + 66/440 = 3 + 33/220 = 3 + 3/20 = 3.15

So r = 3.15 cm

But question asks for diameter, so d = 2r = 6.3 cm

Check: 2πr = 2*(22/7)*3.15 = (44/7)*3.15

3.15 = 315/100 = 63/20

So (44/7)*(63/20) = (44*63)/(7*20) = (44*9)/20 = 396/20 = 19.8 — yes, correct.

So diameter = 6.3 cm

Q7: Sprinkler sprays 7m in all directions — so radius = 7m

Outer edge of wet grass is the circumference: 2πr = 2*(22/7)*7 = 44 m

Nice.

Q8: Area, radius 7cm: πr² = (22/7)*49 = 22*7 = 154 cm²

Q9: Radius 2.1m, area = πr² = (22/7)*(2.1)^2

2.1^2 = 4.41

(22/7)*4.41 = 22 * 0.63 = ? Because 4.41 / 7 = 0.63

22 * 0.63 = 22*0.6 + 22*0.03 = 13.2 + 0.66 = 13.86 m²

Or: (22/7)*4.41 = (22*4.41)/7

4.41 / 7 = 0.63, times 22 = 13.86

Q10: Radius 7km, area = πr² = (22/7)*49 = 154 km²

Now back to Q2 and Q3.

Q2: radius 10m, circumference = 2*(22/7)*10 = 440/7 ≈ 62.857 m

Since it's measurement, probably round to two decimals: 62.86 m

But let's see if 440/7 is acceptable — but in box, likely decimal.

Similarly, Q3: 2*(22/7)*4 = 176/7 ≈ 25.1428... → 25.14 km

But in Q5,6,7,8,9,10 we got nice numbers except Q2,3.

Q1 is 88, Q4 is 3:2, Q5 is 10.5, Q6 is 6.3, Q7 is 44, Q8 is 154, Q9 is 13.86, Q10 is 154.

Q9 is 13.86, which is decimal, so decimals are fine.

So for Q2: 440/7 = 62.857... → typically rounded to 62.86 m

But let's calculate exactly: 440 ÷ 7 = 62.857142... so to two decimals, 62.86

Similarly, Q3: 176 ÷ 7 = 25.142857... → 25.14 km

But is there a better way? Perhaps they expect fractional, but I think decimal is fine.

Note that in Q9, we have 13.86, which is exact with π=22/7: (22/7)*(2.1)^2 = (22/7)*(441/100) = (22*441)/(7*100) = (22*63)/100 = 1386/100 = 13.86 — exact.

Similarly, for Q2: 2*(22/7)*10 = 440/7 = 62 6/7, which is 62.857..., not terminating, so must round.

In educational contexts, often they round to two decimals.

So I'll go with that.

Now summarize all answers:

1. 88 cm
2. 62.86 m (but let's confirm calculation: 2 * 3.1416 * 10 ≈ 62.832, but with 22/7=3.142857, 2*3.142857*10=62.85714, so 62.86 when rounded to two decimals)
However, in some systems, they might expect 62.8 or something, but I think 62.86 is fine.

To be precise, since 440/7 = 62.857..., and if we round to nearest hundredth, it's 62.86.

Similarly for Q3: 176/7 = 25.142857... → 25.14

But let's double-check Q3: radius 4km, C=2*π*4=8π, with π=22/7, 8*22/7=176/7≈25.1428, yes.

Now for the final answers, I'll list them.

Also, Q4 is ratio, so "3:2"

Q5: 10.5 cm

Q6: diameter 6.3 cm

Q7: 44 m

Q8: 154 cm²

Q9: 13.86 m²

Q10: 154 km²

Now, for Q2 and Q3, I'll use two decimal places.

But let me see if the worksheet has any clue — in Q5, dimensions are given as 18.7 and 14.3, which have one decimal, so perhaps answers should have one or two decimals.

In Q6, side 6.6 cm, one decimal, answer diameter 6.3 cm, one decimal.

In Q9, radius 2.1m, one decimal, area 13.86, two decimals — because squaring gives more digits.

So it's inconsistent, but mathematically correct.

For Q2: 62.86 m (two decimals)

Q3: 25.14 km (two decimals)

I think that's acceptable.

So compiling all:

1. 88
2. 62.86
3. 25.14
4. 3:2
5. 10.5
6. 6.3
7. 44
8. 154
9. 13.86
10. 154

With units as specified.

Now for the Final Answer section, since it's multiple questions, I need to provide all answers.

The instruction says "Final Answer: [Provide only the final correct answer]", but for multiple questions, probably list them.

Looking back at user request: "Solve the problem accurately." and it's a worksheet with 10 questions.

So I should provide all 10 answers.

In the response format, it says "Final Answer: [Provide only the final correct answer]", implying for the task, but since it's multiple, I'll list them numbered.

Perhaps write as a list.

I think it's clear.

So here we go.