Question

The radius of a semi-circular garden is 21m. One has to walk ______m to walk all around the garden once?
A) 110
B) 108
C) 170
D) 180

Answer 1

Hint: When someone walks around the garden then the length covered by them would be nothing but the perimeter of the semi-circular garden .Try to calculate the circumference of the semicircle and the straight path along the diameter separately and then add both to get the final result.

Complete step by step Answer:

We just need to calculate the perimeter of the garden and it will be our answer.
As we know the circumference of a circle is $=2\pi r$
But since is it is a semi-circle the circumference will be$=\pi r$
But the semi-circular Garden also has a path along the diameter so it should also be considered.
The diameter of semicircle
$\begin{align}
  & =2r \\
 & =2\times 21 \\
 & =42\text{m} \\
\end{align}$
The circumference of semi-circular Garden $=\pi r$
Here we consider the value of $\pi =\dfrac{22}{7}$and radius is given as 21m.
Therefore, the circumference of semi-circular garden $=\dfrac{22}{7}\times 21$
     \[\begin{align}
  & =22\times 3 \\
 & =66\text{m} \\
\end{align}\]
The total perimeter of Garden circumference of semi-circular Garden length along the diameter
     \[\begin{align}
  & =66+42 \\
 & =108\text{m} \\
\end{align}\]
The answer is B.

Note: Since the radius was a multiple of 7, we should consider $\pi =\dfrac{22}{7}$instead of $\pi =3.14$which makes calculation easy. Additionally, the common mistake made in this question is while calculating the perimeter is that the length of the path along the diameter is neglected.