Question

If the length of circumference of a circle is 60cm more than its diameter then, the length of circumference is
\[\begin{align}
  & A.14\pi cm \\
 & B.28\pi cm \\
 & C.35\pi cm \\
 & D.42\pi cm \\
\end{align}\]

Answer 1

Hint: We will use two basic formulas related to the circle to solve this question. The circumference of the circle of radius r is given by $C=2\pi r$ we will substitute diameter d = 2r and try to get a relation between circumference C and diameter d. After making a linear equation of one variable, we will solve it to get the required result.

Complete step-by-step answer:
Given that, the circumference of the circle is 60cm. The circumference of circle of radius r is given by $C=2\pi r$
Let the diameter of the circle be d. We know that, the value of diameter $d=2r$ where r is the radius. We have circumference \[C=2\pi r\Rightarrow C=\pi d\]
Taking $d=2r$ we get
Circumference \[C=2\pi r\Rightarrow C=\pi d\]
Where d is diameter.
Given that, the circumference of the circle is 60cm more than its diameter.
\[\Rightarrow C=60+d\]

Substituting the value of circumference \[C=\pi d\] we get:
\[\begin{align}
  & \pi d=60+d \\
 & \Rightarrow \pi d-d=60 \\
 & \Rightarrow d\left( \dfrac{22}{7}-1 \right)=60 \\
 & \Rightarrow \dfrac{15}{7}d=60 \\
 & \Rightarrow d=\dfrac{7\times 60}{15} \\
 & \Rightarrow d=28 \\
\end{align}\]
Now, we have diameter d = 28cm and circumference of circle is $C=\pi d$
\[C=28\pi cm\]
Therefore, the circumference \[C=28 \pi cm\]

So, the correct answer is “Option B”.

Note: Another way to solve this question is taking d = 2r and solving, according to the question we have $C=60+2r$ where C is circumference $C=2\pi r$
\[\begin{align}
  & 2\pi r=60+2r \\
 & \Rightarrow \left( 2\pi -2 \right)r=60 \\
 & \Rightarrow \left( 2\times \dfrac{22}{7}-2 \right)r=60 \\
 & \Rightarrow r=\dfrac{60}{30}\times 7 \\
 & \Rightarrow r=14cm \\
\end{align}\]
Then the circumference \[C=2\pi r\Rightarrow C=2\pi \times 14\Rightarrow 28\pi \] which is option B.