Question

A pool is 44.6 m long and 27.6 m wide. If the average depth of water is 8.80 ft, what is the mass (in kg) of water in the pool? Enter your answer in scientific notation.

Answer 1

To find the mass of the water in the pool, convert the depth from feet to meters, calculate the volume in cubic meters, and multiply by the density of water (1000 kg/m³) to get the mass in kilograms. Express the answer in scientific notation.

Step-by-step explanation:

To calculate the mass of the water in the pool, we first need to determine the volume. Since the pool is 44.6 m long and 27.6 m wide, and the average depth is given in feet, we need to convert the depth from feet to meters. There are 0.3048 meters in a foot, so 8.80 feet is equivalent to 8.80 × 0.3048 meters.

Once we have the depth in meters, we can calculate the volume of the pool in cubic meters (m³) by multiplying the length by the width by the depth. After that, to find the mass, we use the fact that the density of water is approximately 1000 kg/m³, so the mass of water is the product of the volume and density. Remember to express the final answer in scientific notation, which will be in the form of a number times 10 to the power of some exponent.

Answer 2

• 3.30 × 10⁶ kg

Step-by-step explanation:

The form of the pool may be approximated to a reactangular prism with height equal to the average depth of water.

1) Dimensions:

• Length: 44.6 m
• Wide: 27.6 m
• Height: 8.80 ft

2) Volume formula

• V = length × width × height

3) Unit conversions

Convert 8.80 ft to meters:

• 1 ft = 0.3048 m ⇒ 1 = 0.3048 m/ft

• 8.80 ft × 0.3048 m/ft = 2.68 m

4) Volume calculation

Substitute the numbers in the formula:

• V = length × width × height = 44.6 m × 27.6 m × 2.68 m ≈ 3,298.97 m³ ≈ 3,300 m³ (it is rounded to three significant digits)

5) Mass of water:

• Density = mass / volume ⇒ mass = density × mass

• Density of water = 1,000 kg / m³

• mass = 3,300 m³ × 1,000 kg / m³ = 3,300,000 kg

6) Scientific notation

Choose the correct number of significant figures:

• Since the three given factors have 3 significant figures, the correct number of significant figures of the volume and the mass is 3.

The mass must be expressed as a power of ten. The mantissa contains only the significant digits, and the number before the decimal point can only have one digit 1 through 9.

• 3,300,000 kg = 3.30 × 10⁶ kg