Question

The volume of a cuboid is \[3456c{m^3}\]. If its length \[ = 24cm\] and breadth \[ = 18cm\], then find its height in cm.
A. $6$
B. $8$
C. $9$
D. $10$

Answer 1

Hint: We know that cuboids have six sides. In this equation we have given the volume of length, breadth and volume of cuboid. We have to find the volume of the cuboid. We have to find the volume of the cuboid. So with the help of formulas to find the volume, we can easily find the unknown quantity, we will put the value of volume, length and breadth. Then we can easily get the height of the cuboid.

Complete step-by-step answer:
The volume of a cuboid $ = 3456c{m^3}$
Length of cuboid $ = 24cm$
Breadth of a cuboid $ = 18cm$
Height of a cuboid $ = ?$
Here, height is an unknown quantity. We will use the formula of cuboid to find the value of volume. We know that the volume of cuboid is equal to the multiplication of its length, breadth and height.
i.e. $Volume = length \times breadth \times height$
So, $3456 = 24 \times 18 \times height$
On right hand side, we will multiply first two terms $24$ and $18$ we get,
$3456 = 432 \times height$
$\dfrac{{3456}}{{432}} = height$
On left hand side $3456$ divided by $432$, we get $8$ i.e.
$\dfrac{{3456}}{{432}} = height$
$8 = h$
i.e. $Height = 8cm$

Therefore, the height of cuboid is $8cm$.

Note: If an object is solid, then the space occupied by such an object is measured, and it termed the volume of the object. On the other hand, if the object is hollow, then the interior is empty, and can be filled with air, or some liquid that will take the shape of its container. In this case, the volume of the substance that can fill the interior is called the capacity of the container.