Question

The length of cuboid is 12 cm, breadth and height are equal and its volume is $432c{m^3} $. The cuboid is cut into 2 cubes, and finds the lateral surface area of each cube.

Answer 1

Hint: After reading the question we can see that two shapes are used in the question that is cube and cuboid. The formula of volume of cuboid is length. breadth. height. and the lateral surface area of the cube is 4. side. side. We have to use this formula to solve the question.

Complete step-by-step answer:

We have,
Length of cuboid = 12cm
Let breadth of cuboid is = x cm
Breadth = height = x cm
Volume of cuboid = $432c{m^3}$
The formula of volume of cuboid = length. breadth. height
Now put the values of length, breadth, and height
 $12cm.xcm.xcm = 432c{m^3} $
$12cm.{x^2} = 432c{m^3} $
After solving the equation, we get
${x^2} = \dfrac{{432}}{{12}}$
Cancel the numerator and denominator
${x^2} = 36$
$x = \sqrt {36} $
$x = 6$
So, we have the breadth and height of cuboid is 6cm
Now the cuboid is cut in 2 cubes along the length
So, the length of each cube $ = \dfrac{{12}}{2}$cm
Length (side) of the cube is = 6cm
Lateral surface area of cube = 4. side. side
$ = 4.6cm.6cm$
$ = 144c{m^2} $

Hence, we have the lateral surface area of each cube that is $144c{m^2} $.

Note: Here students get confused between the breadth and height as the value of it is not given in the question but the question says that they both are equal to each other so we have to let the value of one of them. If the question does not contain the same measures unit then first converts the value meter to centimeter or centimeter to meter. Whenever you find the area, always put $c{m^2} $ and for volume $c{m^3} $.