Question

If the difference between the circumference and the radius of a circle is 37 cm then its diameter equals to
( a ) 28 cm
( b ) 14 cm
( c ) 42 cm
( d ) none of these

Answer 1

Hint: In question it is given that the difference between the circumference and the radius of a circle is 37 cm and we have to find the diameter of a circle so what we will do is we will substitute the formula of circumference and radius r and solve the equation putting it equals to 37 cm.

Complete step-by-step solution:

The radius of a circle denoted by r is the distance of the line from the centre of the circle to the outer edge, and the circumference of a circle is the perimeter of the circle that means a measure of the outer round length of the circle.
The formula to find the circumference is $2\pi r$, where $\pi$ is spelled as pi and is equal to ${\displaystyle \frac{22}{7}}$ or approximately equals to $3.14....$.
Now, in question, it is given that the difference between the circumference and the radius of a circle is 37 cm and we have to find the diameter of a circle.
The diameter of a circle is length equals to twice of the radius that is if d denotes diameter and r denotes radius, then d = 2r.
So, as the difference between the circumference and the radius of a circle is 37 cm, then
$2\pi r-r=37$
Now, taking common factor which is r, outside
$r(2\pi -1)=37$……………..... ( i )
Now, putting value of $\pi$equals to ${\displaystyle \frac{22}{7}}$ in equation ( i ), we get
$r(2\cdot {\displaystyle \frac{22}{7}}-1)=37$
On solving we get
$$r({\displaystyle \frac{44}{7}}-1)=37$$
Taking L.C.M in brackets we get,
$$r({\displaystyle \frac{44-7}{7}})=37$$
On solving, we get
$$r({\displaystyle \frac{37}{7}})=37$$
Taking 7 from denominator on left hand side to numerator on right side we get,
 $$r\times 37=37\times 7$$
On solving we get,
$$r=7$$
So, the radius is equal to 7 cm.
Now, as the discussed diameter of a circle is twice the radius of a circle
So, the diameter of circle $$=2\times r$$……………..…( ii )
Putting the value of r in equation ( ii ), we get
$$2\times 7=14$$ cm
Hence, the diameter of the circle equals 14 cm.

Hence, option ( b ) is correct.

Note: While solving the questions of the circle, one must know the concept of the radius of a circle, the diameter of circle and circumference of the circle, and how to calculate the circumference of the circle. While calculating circumference first see which value of $\pi$, which are 3.14 and ${\displaystyle \frac{22}{7}}$ will give you the most simplest solution and help in the calculation.