Question

If the volume of the cuboid is \[448c{{m}^{3}}\] and its height is 7cm and the base is a square. Find
(1) the side of the square base
(2) surface area of the cuboid

Answer 1

Hint: We know that the formula for volume of cuboid is given by \[V=l\times b\times h\] and formula for surface area of cuboid is given by \[S=2(lb+bh+hl)\] where l, b, h are length, breadth, height respectively. By substituting the value of height in the volume of a cuboid we will get the side of the square base.

Complete step-by-step solution -

Given, the volume of cuboid is \[448c{{m}^{3}}\] and height of cuboid is 7cm
(1).We know that the formula for volume of cuboid is given by
\[V=l\times b\times h\]
  l stands for length
 b stands for breadth
 h stands for height
volume of cuboid V= \[\Rightarrow l\times b\times 7=448c{{m}^{3}}\]. . . . . . . . . . . . . . . . . . . . . .(1)
\[l\times b=64c{{m}^{2}}\]. . . . . . . . .. . . . . . . . . . .(2)
Since the base is square. We know that in a square \[l=b\]
Substituting \[l=b\] in equation (2) we will get the side of square as follows,
\[{{l}^{2}}=64c{{m}^{2}}\]
\[l=b=8cm\]
So, the side of square base obtained is 8cm
(2).we know that the formula for surface area of cuboid is given by
Surface area = \[=2(lb+bh+hl)\]
\[=2(8\times 8+8\times 7+8\times 7)\]
\[=2(64+56+56)\]
\[=352c{{m}^{2}}\]

Note: A cuboid is a three dimensional shape with length, width and a height. The cuboid shape has 6 faces. The each face of a cuboid is rectangle, and all of the cuboid corners are 90 degrees. So, we can say that cuboid has a shape of a rectangular box. The book is an example of the cuboid shape we used in our daily life.