Question

Two rectangular boxes have the same height and lenght, but different widths as shown in the figure.

The difference in the volumes of the boxes is $360c{m}^3.$
What is the height of the boxes?

• A. 18 cm
• B. 15 cm
• C. 16 cm
• D. 14 cm

Answer 1

The correct option is B

15 cm

.
Volume of a cuboid = $l\times b\times h$
where, l = length of the cuboid
b = width of the cuboid
h = height of the cuboid

Let the volume of first box be V1 and second box be V2:
$\Rightarrow V1=8\times 9\times h=72h\text{cubic cm (l, b, h for both boxes are provided)}\Rightarrow V2=8\times 12\times h=96h\text{cubic cm}$
Given :
V2-V1=360 cubic cm
$\Rightarrow$ 96h - 72h = 360
$\Rightarrow$ 24h = 360
$\Rightarrow h=\left(\frac{360}{24}\right)=15cm.$