Find the AREA and CIRCUMFERENCE of a CIRCLE - 60 QUESTIONS across ... - Free Printable

Let’s solve the first problem from the worksheet: Question 1.

We are given a circle with radius = 7 cm.

We need to find:
- Area (A) of the circle
- Circumference (C) of the circle

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Step 1: Recall the formulas

From the top of the worksheet, we’re reminded:

> Area (A) of a circle = πr²
> Circumference (C) = 2πr or πd

Since we’re given the radius (r), we’ll use:

- A = π × r²
- C = 2 × π × r

We’ll use π ≈ 3.141592653589793 (as shown in the example on the sheet).

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Step 2: Plug in r = 7 cm into the area formula

A = π × (7)²
A = π × 49
A = 3.141592653589793 × 49

Let’s calculate that:

3.141592653589793 × 49 = ?

Break it down:

3 × 49 = 147
0.141592653589793 × 49 ≈ let’s compute:

0.1 × 49 = 4.9
0.04 × 49 = 1.96 → total so far: 4.9 + 1.96 = 6.86
0.001592653589793 × 49 ≈ 0.078 (approx)

So adding up: 147 + 6.86 + 0.078 ≈ 153.938

But let’s do exact multiplication:

3.141592653589793 × 49 = 153.93804002589986

Rounded to 2 decimal places (as per instructions: “Work out... to 2 d.p.”):

→ Area = 153.94 cm²

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Step 3: Now calculate circumference

C = 2 × π × r
C = 2 × 3.141592653589793 × 7

First, 2 × 7 = 14
Then, 14 × 3.141592653589793

Calculate:

10 × 3.141592653589793 = 31.41592653589793
4 × 3.141592653589793 = 12.566370614359172
Add them: 31.41592653589793 + 12.566370614359172 = 43.9822971502571

Rounded to 2 decimal places:

→ Circumference = 43.98 cm

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Final Check:

In the example at the top, they used r=5 and got:

A = 78.54 (which is π×25 ≈ 78.54) — correct
C = 31.42 (which is 2π×5 ≈ 31.42) — correct

Our method matches theirs.

For r=7:

A = π×49 ≈ 153.94 ✔
C = 2π×7 ≈ 43.98 ✔

Units: cm² for area, cm for circumference — included as instructed.

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Final Answer:
A = 153.94 cm²
C = 43.98 cm