Question

What percentages of cubes are removed from the figure (I) to get figure (II)?

\[\begin{align}
  & A)18\dfrac{4}{5}\% \\
 & B)27\dfrac{3}{11}\% \\
 & C)18\dfrac{3}{4}\% \\
 & D)21\dfrac{3}{7}\% \\
\end{align}\]

Answer 1

Hint: First of all, we should understand the question. Now we will carefully observe both the figures and count the number of cubes present in each figure. Now it is clear we should find the percentage of cubes removed. So, let us find the difference of cubes in figure 1 and figure 2. Now let us divide this difference of cubes by the number of cubes in figure 1. So, we can find the percentage of cubes removed by using the formulae that
\[\text{Percentage of cubes removed from figure 1 to get figure =}\dfrac{number\text{ of cubes in figure 1- number of cubes in figure 2}}{number\text{ of cubes in figure 1}}\times 100\]We know that the percentage of a certain quantity can be represented by the symbol %.

Complete step-by-step solution:

Now we will carefully observe both the figures and count the number of cubes present in each figure.
By carefully observing both the figures we can say that
The number of cubes present in figure (I) is 32 and the number of cubes present in figure (II) is 26.
We know that
\[\text{Percentage of cubes removed from figure 1 to get figure =}\dfrac{number\text{ of cubes in figure 1- number of cubes in figure 2}}{number\text{ of cubes in figure 1}}\times 100\]
So, let us find the difference between the number of cubes from figure 1 to figure 2.
\[\Rightarrow \text{ Number of cubes in figure 1- Number of cubes in figure 2}=32-26=6\]
\[\begin{align}
  & \Rightarrow \text{Percentage of cubes removed from figure 1 to get figure 2=}\dfrac{6}{32}\times 100 \\
 & \Rightarrow \text{Percentage of cubes removed from figure 1 to get figure }2=\dfrac{75}{4} \\
 & \Rightarrow \text{Percentage of cubes removed from figure 1 to get figure }2=18\dfrac{3}{4} \\
\end{align}\]
We know that the percentage is represented by the symbol %. So, we can say that the percentage of cubes removed from figure (I) to get figure (II) is equal to $18\dfrac{3}{4}\%$.
Hence option C is correct.

Note: While counting the number of cubes we should be careful if we even miss a single cube the answer will completely vary from the actual answer. So, students should recheck more than one time whether they counted the number of cubes in a correct manner or not. If any counting mistake, it should be rectified by the student immediately to have a correct answer.