Question

I need some help on these problems:

1) A swimming pool measures 9.0 m long by 3.5 m wide by 1.75 m deep. What mass of water in metric tons (1 metric ton = 1000 kg) does the pool contain when filled? The density of the water is 0.991 g/cm3.

2) If a liquid has a density of 1.17 g/cm3, how many liters of the liquid have a mass of 3.75 kg?

3) When a sample of a metal alloy that has the mass of 9.65 g is placed into a graduated cylinder containing water, the volume reading in the cylinder increases from 16.0mL to 19.5mL. What is the density of the alloy sample in grams per cubic meter?

Answer 1

2.vol 3.75/1.17 = 3.205 cm^3

Answer 2

Q1. The answer is 54.629 metric tons

A mass (m) of a liquid is its density (D) multiplied by its volume (V): m = D · V
Step 1. Calculate the volume (V) of the swimming pool.
Step 2. Calculate the mass (m) of the water.
Step 3. Convert the mass into the metric tones.

Step 1.
V = w * l * h (w - weight, l - length, h - height)
w = 3.5 m
l = 9 m
h = 1.75 m
_______
V = 3.5 * 9 * 1.75
V = 55.125 m³

Step 2:
m = D * V
D = 0.991 g/cm³
1 g = 0.001 kg
1 cm³ = 0.000001 m³
D = 0.991g / 1cm³ = 0.991 * 0.001 kg / 0.000001 m³ = 991 kg/m³
V = 55.125 m³
_________
m = 991 * 55.125
m = 54628.875 kg ≈ 54629 kg

Step 3.
Since 1 metric ton is 1000 kg, how many metric tons are 54629 kg?
1 mt : 1000 kg = x : 54629 kg
x = 1 mt : 1000 kg * 54629 kg
x = 54.629 metric tons



Q2. The answer is 3.2 l.

Step 1. Convert g/cm³ into kg/dm³ (because 1 l = 1 dm³)
Step 2. Calculate how many liters of the liquid have a mass of 3.75 kg using the proportion

Step 1.
D = 1.17 g/cm3
1 g = 0.001 kg
1 cm³ = 0.001 dm³
D = 1.17 * 0.001 kg / 0.001 dm³ = 1.17 kg/dm³

Step 2.
If 1.17 kg is in 1 dm³, 3.75 kg are in how many dm³:
1.17 kg : 1 dm³ = 3.75 kg : x
x = 3.75 kg * 1 dm³ : 1.17 kg
x = 3.2 dm³
1 dm³ = 1 l
x = 3.2 l



Q3. The answer is 2757140 g/m³

Step 1. Calculate the increased volume and convert units into liters.
Step 2. Calculate the density of the alloy sample and convert units into g/m³

Step 1.
The difference in the volume of the water in cylinder is:
V = 19.5 ml - 16 ml = 3.5 ml
1 ml = 0.001 l
V = 3.5 * 0.001 l = 0.0035 l

Step 2.
A density (D) of an object with mass m and volume V is:
D = m/V

We have:
D = ?
m = 9.65 g
V = 0.0035 l
______
D = 9.65/0.0035 g/l = 2757.14 g/l
1 l = 1 dm³ = 0.001 m³
D = 2757.14 g/0.001 m³ = 2757140 g/m³