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Question 1

A)A rectangular prism has a base that is 10 inches wide and 1 foot long, and is 2.5 inches deep. Find the volume of the prism.(1 point)
The rectangular prism has a volume of $$ in.3.
Question 2
A)A triangular prism has a volume of 500 cubic centimeters. Determine the height of the prism if the bases of the prism have a height of 10 centimeters and a base length of 8 centimeters. Enter your answer as a decimal, if needed. Be sure to enter the exact value.(1 point)
The prism has a height of $$ centimeters.
Question 3
A)A storage unit has 750 cubic feet of space. Determine the depth of the unit to the nearest whole number if the measurements of one wall are 9 feet by 12 feet.(1 point)
The depth of the storage unit is approximately $$ feet.
Question 4
A)The volume of a nickel (a 5-cent coin) is 0.719 cm3. A roll of nickels is cylindrical and holds $2 worth of nickels. What is the volume of nickels in a roll? Enter your answer to the nearest hundredth.(1 point)
A $2 roll of nickels has a volume of $$ cm3.
Question 5
A)A rectangular swimming pool is 25 yards long and 20 yards wide. The first 10 yards has a depth of 4 feet and the remaining 15 yards has a depth of 8 feet. A circular hot tub that is 4 feet deep and has a diameter of 3 yards is attached to the deep end of the pool. What volume of water is needed for the owner to fill the pool and hot tub? Provide your answer in cubic feet. Enter your answer to the nearest thousandth.(1 point)
The owner will need $$ cubic feet of water to fill the pool and hot tub.

1 answer

Let's solve each question step by step:

Question 1:

Find the volume of a rectangular prism.

  1. Base dimensions: Width = 10 inches, Length = 1 foot (12 inches), Depth = 2.5 inches.
  2. Volume \( V \) of a rectangular prism = Base Area × Depth.
    • Base Area = Width × Length = \( 10 , \text{in} \times 12 , \text{in} = 120 , \text{in}^2 \).
  3. Now calculate the volume: \[ V = 120 , \text{in}^2 × 2.5 , \text{in} = 300 , \text{in}^3. \]

Answer: The rectangular prism has a volume of 300 in³.

Question 2:

Determine the height of the prism if the volume is 500 cm³.

  1. Volume \( V \) of a triangular prism = Base Area × Height.
  2. Base Area of triangle = 0.5 × Base × Height of triangle.
    • Base = 8 cm, Height of triangle = 10 cm.
    • Base Area = \( 0.5 × 8 , \text{cm} × 10 , \text{cm} = 40 , \text{cm}^2 \).
  3. Now, use the volume to find the height \( H \): \[ 500 , \text{cm}^3 = 40 , \text{cm}^2 \times H \implies H = \frac{500 , \text{cm}^3}{40 , \text{cm}^2} = 12.5 , \text{cm}. \]

Answer: The prism has a height of 12.5 centimeters.

Question 3:

Determine the depth of a storage unit.

  1. Volume = Length × Width × Depth.
  2. Given volume = 750 ft³, Length = 9 ft, Width = 12 ft.
  3. Solve for depth \( D \): \[ 750 = 9 \times 12 \times D \implies 750 = 108D \implies D = \frac{750}{108} \approx 6.944 \implies D \approx 7 , \text{ft} , (\text{to nearest whole number}). \]

Answer: The depth of the storage unit is approximately 7 feet.

Question 4:

Find the volume of nickels in a roll.

  1. A nickel has a volume of 0.719 cm³.
  2. $2 in nickels = 2 dollars / 0.05 dollar per nickel = 40 nickels.
  3. Volume of nickels in a roll: \[ \text{Total Volume} = 40 \times 0.719 , \text{cm}^3 = 28.76 , \text{cm}^3. \]

Answer: A $2 roll of nickels has a volume of 28.76 cm³.

Question 5:

Find the volume of water to fill the pool and hot tub.

  1. Volume of the pool:

    • First section: \( \text{Volume} = 10 , \text{yds} \times 20 , \text{yds} \times 4 , \text{ft} = 800 , \text{ft}^3 \).
    • Second section: \( \text{Volume} = 15 , \text{yds} \times 20 , \text{yds} \times 8 , \text{ft} = 2400 , \text{ft}^3 \).
    • Total volume of the pool = \( 800 + 2400 = 3200 , \text{ft}^3 \).

  2. Volume of the hot tub:

    • Volume of the cylindrical hot tub \((\text{Circumference} = \pi r^2 h)\).
    • Diameter = 3 yards → Radius = 1.5 yards.
    • Convert to feet: Radius = 1.5 yards = 4.5 feet.
    • Volume = \( \pi (4.5^2) \times 4 = \pi (20.25) \times 4 \approx 254.47 , \text{ft}^3 \).

  3. Total volume of water needed: \[ \text{Total Volume} = 3200 + 254.47 \approx 3454.47 , \text{ft}^3. \]

Round it to the nearest thousandth.

Answer: The owner will need approximately 3454.470 cubic feet of water to fill the pool and hot tub.