Question

A rectangular juice box contains 720 millilitres of apple juice. The box is 12 cm high and 15 cm wide. What is the length of the juice box (1 millilitre = 1 cubic centimetre)?

Answer 1

Hint: To find the length of the juice box, we will first draw a figure of a solid cuboid, with the height as 12 cm and width as 15 cm. We will then assume some variable for the length of this cuboidal juice box. It is given that 1 millilitre = 1 cubic centimetre. We know the volume of the juice box. The units of the volume given is millilitres. We can convert it as a cubic centimetre with the help of the conversion. Now, we know that the volume of the cuboid is given as V = lbh, where l is the length, b is breadth or width and h is the height of the cuboid. We will substitute the dimensions in the above relations and find the length of the juice box.

Complete step-by-step answer:
It is given that the height of the juice box is 12 cm and that the width of the box is 15 cm.
Let the length of the cuboidal juice box be l.
Now, we will draw a figure based on these dimensions.
The figure of the juice box will be as follows:

It is given that the juice box contains 720 millilitres of apple juice. This means the volume of the juice box is 720 millilitres.
Now, from the question itself we know that 1 millilitre = 1 cubic centimetre.
Therefore, the converted volume is 720 cubic centimetres.
We know that the volume of any cuboid is given by the relation V = lbh, where l is the length, b is breadth or width and h is the height of the cuboid.
Now, we will substitute the known values in the above relation.
$\Rightarrow $ 720 = l(12)(15)
$\Rightarrow $ 180(l) = 720
$\Rightarrow $ l = 4
Therefore, the length of the juice box is 4 cm.

Note: Students need to be careful about the units of the dimensions when solving the problems related to volume and surface area. The unit needs to be the same on both sides of equal to sign.