Question

The area of a circle is 346.5 cm2. Find its circumference (in cm).

A) 132 B) 38 C) 66 D) 76

Answer 1

$\huge{\boxed{\rm \red{G}\blue{i}\pink{v}\green{e}\purple{n}:}}$

The area of a circle is 346.5 cm²

$\huge{\boxed{\sf \red{To}\ \blue{be}\ \pink{Found}\green{:}\purple{-}}}$

The circumference of the circle (in cm)

The formula for finding the circumference of a circle -

$\huge{\boxed{\boxed{\tt \blue{2 \pi r}}}}$

[ ∵ In which 'r' is the 'radius' of the circle]

So we need the radius of the circle first,

We can get the radius of the circle from the area formula.

$\implies \bf \pi r^{2} = 346.5 \\ \\ \implies \frac{22}{7} \times r^{2} = 346.5 \\ \\ \implies r^{2} = 364.5 \times \frac{7}{22} \\ \\ \implies r^{2} = \frac{2425.5}{22} \\ \\ \implies r^{2} = 110.25 \\ \\ \implies r = \sqrt{110.25} \\ \\ \implies r = 10.5cm$

So,

$\boxed{\red{\tt radius\ of\ circle = \blue{\boxed{10.5cm}}}}$

Now,

Circumference of the circle

$\bf = 2 \times \frac{22}{7} \times 10.5 \\ \\ \bf = \frac{44}{7} \times 10.5 \\\\ \bf = \frac{462}{7} = 66cm$

Hence

Option C) 66 cm is correct.

The circumference of the circle = 66cm

Answer 2

Given:

• Area of circle = 346.5 cm²

To find:

• Circumference of circle

Solution:

Given

Area of circle = 346.5 cm²

That means ↓

πr² = 346.5

r² = 346.5/π

r² = 346.5/3.14

r² = 110.25

r = √110.25

r = 10.5

__________

Now, finding circumference using ↓

Circumference = 2πr

→ C = 2(3.14)(10.5)

→ C = 65.94 ≈ 66 cm

Hence, circumference of circle = 66 cm