Question

the circumference of a circle exceeds its radius by 37 cm find the diameter of circle using the formula of Pi

Answer 1

this answer was quite easy and the solution above is correct

Answer 2

Answer:

Circumference of a circle is given by:

$C = 2\pi r$

where

C is the circumference of a circle

r is the radius of the circle

As per the statement:

the circumference of a circle exceeds its radius by 37 cm.

⇒$C =r+37$

⇒$2\pi r = r+37$

Subtract r from both sides we get;

$2\pi r -r= 37$

or

$r(2 \pi-1) =37$

Use the value of $\pi = \frac{22}{7}$

$r(2 \cdot \frac{22}{7}-1) =37$

⇒$r(\frac{44}{7}-1) = 37$

⇒$r(\frac{37}{7}) =37$

Divide both sides by 37 we get;

$\frac{r}{7} = 1$

Multiply both sides by 7 we get;

r = 7 cm

We know diameter of circle(d) = 2r

then:

$d = 2(7) = 14 cm$

Therefore, the diameter of circle is 14 cm