Question

If the base of rectangular prism remains constant and the measures of the lateral edges are halved then by how much percent its volume will be reduced?

Answer 1

Hint: The rectangular prism is a cuboidal shaped 3D solid and we can calculate the volume of the cuboid as $l\times b\times h$. Here, l represents length, b represents breadth and h represents height. We will form a relation between the initial and the new volume of the rectangular prism from the condition given in the question and then we will solve the question to find the percentage decrease in the volume, using the formula, $\dfrac{\text{volume decreased}}{\text{initial volume}}\times 100$.

Complete step-by-step answer:
It is given that the base of a right rectangular prism remains constant and the measures of the lateral edges are halved and we have been asked to find by how much percent its volume will be reduced.
So, we are given a rectangular prism which means, it is a cuboidal shaped 3D solid object having 6 faces. We can represent it as follows.

Now, we know that volume of a cuboid can be calculated by using the formula, $l\times b\times h$, where, l represents length, b represents breadth and h represents height. So, initially the volume of the rectangular prism will be, let’s say x cubic unit. It means that,
x = $l\times b\times h$
Now, it is given in the question that the base of the rectangular prism remains constant and the measures of the lateral edges are reduced to half. This means that the length and breadth remains constant but the height is reduced to half. So, we can show it as follows.

So, we get the new volume of the rectangular prism as,
\[l\times b\times \dfrac{h}{2}\]
Now, if we compare the volume of the rectangular prism before and after the change, we get,
New volume of rectangular prism = $\dfrac{1}{2}$ (initial volume of rectangular prism)
We will assume the initial volume of the rectangular prism as 100. As we know that the volume of the rectangular prism is halved, we will get the new volume as 50. So, we can see that the decrease in volume is 50. From this, we will calculate the decrease in the volume of the rectangular prism as,
Percentage decrease in the volume = $\dfrac{\text{volume decreased}}{\text{initial volume}}\times 100$
Percentage decrease in the volume = $\dfrac{50}{100}\times 100=50\%$
Therefore, we get that the volume of the rectangular prism is reduced by 50%.

Note: While solving this question, some students may not understand what a rectangular prism is, as they think that prism is only possible for triangles. So, the students must know that the rectangular prism is nothing but a cuboid in order to solve this question. Also, by just looking at the comparison of the initial and the new volume, we can see that the new volume is half the initial volume, so we can say that the decrease in the volume is 50%.