Question

If all the edges of rectangular prism are doubled and its shape is left unchanged, then the volume increases
(a) 2 times
(b) 3 times
(c) 4 times
(d) 8 times

Answer 1

Hint: First, we will draw a rectangular prism with length l, breadth b and height h. Then, we will find the volume of prism using the formula $volume=length\times breadth\times height$ . Then, we will double the edges, so we will get as 2l, 2b, 2h. Again, we will find the volume of this and will compare it with the original volume.

Complete step-by-step answer:
Here, we will first draw a figure of rectangular prism which is known as cuboid. So, we get figure as

We have assumed length, breadth, and height of cuboid as l, b, h respectively. Now, we know the volume of cuboid is given as
$volume=length\times breadth\times height$
So, on substituting the value we get as
$volume=l\times b\times h=lbh$ …………………………(1)
Now, we are told that is edges of prism is doubled i.e. if length, breadth, and height is double then we get figure as
 

Now, we volume as
$volume=length\times breadth\times height$
On putting the values i.e. 2l, 2b, 2h we get as
$volume=2l\times 2b\times 2h=8lbh$ ………………………(2)
Now, we will compare equation (1) with equation (2) so, we get as
$lbh=8lbh$
Thus, we can say that after edges are doubled, we get volume 8 times to that of original volume.
Hence, option (d) is the correct answer.

Note: Remember that prism have 6 faces i.e. it is a three-dimensional figure. Do not draw as a simple rectangle and calculate volume which will be 4 times to that of original volume which is wrong. So, first understand the difference between a simple rectangle and rectangular prism. Also, we can calculate using length, breadth and height as 1cm. On doubling, we get length, breadth and height as 2cm. Thus, we will get the same answer.