Question

1. a large rectangular swimming pool is 1,000 feet (ft.) long, 100 ft. wide, and 10 ft. deep. the pool is filled to the top with water.

a. what is the area of the surface of the water in the pool?

b. how much water does the pool hold?

c. express your answers to the previous two questions as powers of 10.

review problems

1. a taxi service charges $1.00 for the first \LXI0 mile (mi.) then $0.10 for each additional \\(\frac{1}{10}\\) mi. after that.

fill in the table with the missing information then determine if this relationship between distance traveled and price of the trip is a proportional relationship.

distance traveled (mi.)	price ($)
2
\\(3\frac{1}{10}\\)
10

Explanation:

Problem 2

Part a

Step1: Identify the shape of the water surface

The surface of the water in a rectangular pool is a rectangle. The formula for the area of a rectangle is \( A = l \times w \), where \( l \) is the length and \( w \) is the width.

Step2: Substitute the given values

Given \( l = 1000 \) ft and \( w = 100 \) ft. So, \( A = 1000 \times 100 \).

Step3: Calculate the area

\( 1000 \times 100 = 100000 \) square feet.

Step1: Identify the formula for the volume of a rectangular prism

The volume \( V \) of a rectangular prism (which the pool is) is given by \( V = l \times w \times h \), where \( h \) is the height (depth in this case).

Step2: Substitute the given values

Given \( l = 1000 \) ft, \( w = 100 \) ft, and \( h = 10 \) ft. So, \( V = 1000 \times 100 \times 10 \).

Step3: Calculate the volume

\( 1000 \times 100 \times 10 = 1000000 \) cubic feet.

Step1: Express the area as a power of 10

We know that \( 100000 = 10^5 \) (since \( 10^5 = 10 \times 10 \times 10 \times 10 \times 10 = 100000 \)).

Step2: Express the volume as a power of 10

We know that \( 1000000 = 10^6 \) (since \( 10^6 = 10 \times 10 \times 10 \times 10 \times 10 \times 10 = 1000000 \)).

Answer:

The area of the surface of the water is \( 100000 \) square feet.

Part b