Question

chapter 9 test

1. a swimming pool has a volume of 43,130 cubic feet. how many gallons of water does the pool hold?

the pool holds approximately \boxed{32200} (1) of water.
(round to the nearest whole number as needed.)
(1) \bigcirc gallons²
\bigcirc gallons³
\bigcirc gallons
7.
vert the given celsius temperature to its equivalent temperature on the fahrenheit scale. use $c = \frac{5}{9}(f - 32)$ or $f = \frac{9}{5}c + 32$
$49^\circ$c
$49^\circ$c = \boxed{} $^\circ$f
(round to the nearest tenth as needed.)
use dimensional analysis to convert the quantity to the indicated units.
12 inches (in.) = 1 foot (ft)
3 feet = 1 yard (yd)
1 yard = 36 inches

Explanation:

Problem 6:

Step1: Identify conversion factor

From the table, 1 cubic foot ≈ 7.48 gallons. The pool's volume is 43,130 cubic feet.

Step2: Calculate gallons

Multiply the volume in cubic feet by the conversion factor: \( 43130 \times 7.48 \)
First, calculate \( 43130 \times 7.48 \):
\( 43130 \times 7 = 301910 \)
\( 43130 \times 0.48 = 20702.4 \)
Add them together: \( 301910 + 20702.4 = 322612.4 \) (Wait, the handwritten calculation used 7.48, but let's check the correct multiplication: \( 43130 \times 7.48 = 43130 \times \frac{748}{100} = \frac{43130 \times 748}{100} \))
Wait, maybe the table had 1 cubic foot ≈ 7.48 gallons? Wait, the user's handwritten calculation was \( 43130 / 7.48 \), which is wrong. Wait, no—wait, the table: "1 cubic yard about 200 gallons, 1 cubic foot about 7.48 gallons"? Wait, no, looking at the table: "Volume in Cubic Units" and "Capacity". Wait, the first row: 1 cubic yard about 200 gallons? No, maybe the user misread. Wait, the correct conversion: 1 cubic foot of water is approximately 7.48 gallons. So to convert cubic feet to gallons, multiply by 7.48. Wait, but the handwritten calculation is dividing by 7.48, which is incorrect. Wait, maybe the table was misread. Wait, let's re-express:

Wait, the problem: "A swimming pool has a volume of 43,130 cubic feet. How many gallons of water does the pool hold?"

From the table, "1 cubic foot" has a capacity of "about 7.48 g" (gallons? Wait, maybe the table says 1 cubic foot ≈ 7.48 gallons. So the correct formula is gallons = cubic feet × 7.48.

But the handwritten calculation is \( 43130 / 7.48 \), which is wrong. Wait, maybe the table was "1 cubic yard ≈ 200 gallons" and "1 cubic foot ≈ 7.48 gallons"—no, 1 cubic yard is 27 cubic feet, so 200 gallons per cubic yard would be 200/27 ≈ 7.407 gallons per cubic foot, close to 7.48. Maybe the table has a typo, but let's go with the correct method:

Correct step:

Step1: Conversion factor

1 cubic foot (ft³) ≈ 7.48 gallons (gal)

Step2: Multiply volume by conversion factor

Gallons = 43130 ft³ × 7.48 gal/ft³

Calculate that:

43130 × 7.48 = 43130 × (7 + 0.48) = 43130×7 + 43130×0.48 = 301910 + 20702.4 = 322612.4 gallons

But the handwritten answer is 32261 (wait, 43130 / 7.48 ≈ 5766, which is wrong). Wait, maybe the table was "1 cubic foot ≈ 7.48 gallons" but the user thought it was "1 cubic yard ≈ 7.48 gallons", which is wrong. Alternatively, maybe the table had "231 cubic inches ≈ 1 gallon", but 1 cubic foot is 12×12×12=1728 cubic inches, so 1728/231 ≈ 7.48 gallons, which matches. So 1 cubic foot = 1728 cubic inches, and 231 cubic inches = 1 gallon, so 1 cubic foot = 1728/231 ≈ 7.48 gallons. So the correct calculation is 43130 × 7.48 ≈ 322612 gallons. But the handwritten answer is 32261, which is wrong. Wait, maybe the table was "1 cubic yard ≈ 200 gallons" and the user confused cubic yard and cubic foot. 1 cubic yard = 27 cubic feet, so 200 gallons per cubic yard is 200/27 ≈ 7.407 gallons per cubic foot. If we use [SSE onError error]

Answer:

Step1: Identify conversion factor

From the table, 1 cubic foot ≈ 7.48 gallons. The pool's volume is 43,130 cubic feet.

Step2: Calculate gallons

Multiply the volume in cubic feet by the conversion factor: \( 43130 \times 7.48 \)
First, calculate \( 43130 \times 7.48 \):
\( 43130 \times 7 = 301910 \)
\( 43130 \times 0.48 = 20702.4 \)
Add them together: \( 301910 + 20702.4 = 322612.4 \) (Wait, the handwritten calculation used 7.48, but let's check the correct multiplication: \( 43130 \times 7.48 = 43130 \times \frac{748}{100} = \frac{43130 \times 748}{100} \))
Wait, maybe the table had 1 cubic foot ≈ 7.48 gallons? Wait, the user's handwritten calculation was \( 43130 / 7.48 \), which is wrong. Wait, no—wait, the table: "1 cubic yard about 200 gallons, 1 cubic foot about 7.48 gallons"? Wait, no, looking at the table: "Volume in Cubic Units" and "Capacity". Wait, the first row: 1 cubic yard about 200 gallons? No, maybe the user misread. Wait, the correct conversion: 1 cubic foot of water is approximately 7.48 gallons. So to convert cubic feet to gallons, multiply by 7.48. Wait, but the handwritten calculation is dividing by 7.48, which is incorrect. Wait, maybe the table was misread. Wait, let's re-express:

Wait, the problem: "A swimming pool has a volume of 43,130 cubic feet. How many gallons of water does the pool hold?"

From the table, "1 cubic foot" has a capacity of "about 7.48 g" (gallons? Wait, maybe the table says 1 cubic foot ≈ 7.48 gallons. So the correct formula is gallons = cubic feet × 7.48.

But the handwritten calculation is \( 43130 / 7.48 \), which is wrong. Wait, maybe the table was "1 cubic yard ≈ 200 gallons" and "1 cubic foot ≈ 7.48 gallons"—no, 1 cubic yard is 27 cubic feet, so 200 gallons per cubic yard would be 200/27 ≈ 7.407 gallons per cubic foot, close to 7.48. Maybe the table has a typo, but let's go with the correct method:

Correct step:

Step1: Conversion factor

1 cubic foot (ft³) ≈ 7.48 gallons (gal)

Step2: Multiply volume by conversion factor

Gallons = 43130 ft³ × 7.48 gal/ft³

Calculate that:

43130 × 7.48 = 43130 × (7 + 0.48) = 43130×7 + 43130×0.48 = 301910 + 20702.4 = 322612.4 gallons

But the handwritten answer is 32261 (wait, 43130 / 7.48 ≈ 5766, which is wrong). Wait, maybe the table was "1 cubic foot ≈ 7.48 gallons" but the user thought it was "1 cubic yard ≈ 7.48 gallons", which is wrong. Alternatively, maybe the table had "231 cubic inches ≈ 1 gallon", but 1 cubic foot is 12×12×12=1728 cubic inches, so 1728/231 ≈ 7.48 gallons, which matches. So 1 cubic foot = 1728 cubic inches, and 231 cubic inches = 1 gallon, so 1 cubic foot = 1728/231 ≈ 7.48 gallons. So the correct calculation is 43130 × 7.48 ≈ 322612 gallons. But the handwritten answer is 32261, which is wrong. Wait, maybe the table was "1 cubic yard ≈ 200 gallons" and the user confused cubic yard and cubic foot. 1 cubic yard = 27 cubic feet, so 200 gallons per cubic yard is 200/27 ≈ 7.407 gallons per cubic foot. If we use [SSE onError error]