Question

What percent of the following figure is shaded?

(a) 30
(b) 40
(c) 60
(d) 50

Answer 1

Hint: Firstly, we have to find the fraction of the shaded portion. If there are a total of n regions of which a region is shaded, then the fraction of shaded portion is given by $\dfrac{a}{n}$ . Then, we have to multiply this fraction with 100% to get the percentage of the shaded portion.

Complete step by step answer:
We have to find the percent of the shaded portion. Let us first find the shaded portion. We know that if there are a total of n regions of which a region is shaded, then the fraction of the shaded portion is given by $\dfrac{a}{n}$ .
From the figure, we can see that the total number of sectors is $=5$ .
The number of shaded sectors $=3$ .
Therefore, the shaded portion is given by
$\Rightarrow \dfrac{3}{5}$
Now, we have to convert the above fraction to its percentage form. We know that to convert a number into percentage, we have to multiply it by 100. Therefore, let us multiply $\dfrac{3}{5}$ by 100.
$\begin{align}
  & \Rightarrow \text{Percentage of shaded portion}=\dfrac{3}{5}\times 100\% \\
 & \Rightarrow \text{Percentage of shaded portion}=0.6\times 100\% \\
 & \Rightarrow \text{Percentage of shaded portion}=60\% \\
\end{align}$

So, the correct answer is “Option c”.

Note: Students have a chance of making a mistake by writing the fraction as the total number of sections divided by the number of shaded sections. They may also make mistakes when converting the fraction into percentage by dividing the fraction by 100 instead of multiplying. Students must never forget to write the percentage sign in the last calculation.