Question

How many alarm clocks of size $5cm \times 10cm \times 10cm$ can be packed into a box of size $1m \times \dfrac{1}{2}m \times \dfrac{3}{4}m$ ?

Answer 1

Hint: In this kind of problem we need to approach questions by finding the volume of clocks and the box to find how many clocks can fit inside the box the capacity of the box will be known when we find the volume of it. By dividing it by the volume of the clock.

Complete step by step answer:
Given,
A box size is $1m\times \dfrac{1}{2}m\times \dfrac{3}{4}m$
Finding the volume of the box as it is cuboid
Volume=$l \times b \times h$
Volume of box will be
$\Rightarrow 0.375{{m}^{3}}$
The alarm clock size is
$\Rightarrow 5cm\times 0.10cm\times 0.10m$
The volume of clock or size of one clock
$ = 500c{m^3}$
Finding the number of clocks that can fit in the box.
Divide box volume by clock
Clock is in centimeter box is in meter convert in one unit
Therefore, the alarm clock which can fit in box
$ \Rightarrow \dfrac{{0.375}}{{0.0005}}$
We know that,
$1m=100cm$
Covert meter in cm.
$ =\dfrac{3750000}{5000}$
$ \Rightarrow 750 $

$\therefore$ 750 clocks can be fit in the box.

Note:
In this kind of problem analyze the unit of given parameters if it is not the same convert then solve by finding volume and dividing obtained value the stuff to be fit in the volume of the given box or trunk what-ever given.