Question

A swimming pool measures $50meters$ by $25meters$ . How many grams of water are needed to fill the pool, whose average depth is $7.8feet$ ? Assume the density of water to be $1.0g/ml$.

Answer 1

In order to find grams of water required to fill the pool we first have to convert depth of the pool which is given in feet to meters followed by calculating the volume of water in milliliters and then finally calculating the mass of water.

Complete step by step solution:
There are multiple steps involved in order to calculate the mass of water required to fill the pool,
The steps are as follows,
Converting the depth of the pool from feet to meters
$h = 7.8feet \times \dfrac{{12inches}}{{1feet}} \times \dfrac{{1m}}{{39.37in}} = 2.38m$
Hence the depth of the pool (h) is $2.38m$
Calculating volume of the water
Volume of the water is the product of length, width, and height.
$V = lwh = 50m \times 25m \times 2.38m = 2980{m^3}$
Converting volume of the water to milliliters
$V = 2980{m^3} \times \dfrac{{1000L}}{{1{m^3}}} \times \dfrac{{1000mL}}{{1L}} = 2.98 \times {10^9}mL$
Calculating mass of water
Since we know that,
$Density = \dfrac{{Mass}}{{Volume}} \\\ Mass = Density \times Volume \\\ m = \dfrac{{1.0g}}{{1mL}} \times 2.98 \times {10^9}mL = 3.0 \times {10^9}g$
Hence the mass of water needed to fill the pool is $3 \times {10^9}g$

Additional Information:
The mass concept measures the quantity of matter which exists in an object. It is a quantitative property of an object against the acceleration. The mass and weight of an object are not the same. It gives an idea about how much matter is present in an object. It is a quantitative measure of inertia. Hence, we can say that acceleration is inversely proportional to inertia.

Note:
Make sure to convert the units like depth of the pool from feet to meters and volume of water to milliliters. The volume of water is the product of three variables which is length, width, and height. Density is the most convenient way of obtaining the mass of a substance when the volume is given.