- Find the volume in gallons of cylinder that has radius of 18 feet and depth of 20 feet; Round the answer t0 the hundreds place- 1. 38,000 gal 2. 5,100 gal 3_ 152,200 gal 4. 20,300 gal
The Correct Answer and Explanation is:
To find the volume of a cylinder, we use the formula:V=πr2hV = \pi r^2 hV=πr2h
Where:
- VVV is the volume
- rrr is the radius
- hhh is the height (or depth in this case)
- π≈3.1416\pi \approx 3.1416π≈3.1416
Given:
- Radius r=18r = 18r=18 feet
- Depth h=20h = 20h=20 feet
V=π(18)2(20)=3.1416×324×20=3.1416×6480≈20357.57 cubic feetV = \pi (18)^2 (20) = 3.1416 \times 324 \times 20 = 3.1416 \times 6480 \approx 20357.57 \text{ cubic feet}V=π(18)2(20)=3.1416×324×20=3.1416×6480≈20357.57 cubic feet
Next, convert cubic feet to gallons.
1 cubic foot = 7.4805 gallons20357.57×7.4805≈152224.38 gallons20357.57 \times 7.4805 \approx 152224.38 \text{ gallons}20357.57×7.4805≈152224.38 gallons
Rounded to the hundreds place, the volume is:152,200 gallons\boxed{152,200 \text{ gallons}}152,200 gallons
Correct answer: 3. 152,200 gal
Explanation
To calculate the volume of a cylinder, we use the geometric volume formula: V=πr2hV = \pi r^2 hV=πr2h, where rrr is the radius of the base and hhh is the height or depth. This formula is derived from the idea that the volume of a cylinder is the area of the base (a circle) multiplied by the height.
In this case, the cylinder has a radius of 18 feet and a depth of 20 feet. First, square the radius:
182=32418^2 = 324182=324.
Then multiply by the depth:
324×20=6480324 \times 20 = 6480324×20=6480.
Now multiply by π≈3.1416\pi \approx 3.1416π≈3.1416:
6480×3.1416≈20357.576480 \times 3.1416 \approx 20357.576480×3.1416≈20357.57 cubic feet.
The next step is to convert cubic feet to gallons since the final answer must be in gallons. The conversion factor is:
1 cubic foot = 7.4805 gallons.
So,
20357.57×7.4805≈152224.3820357.57 \times 7.4805 \approx 152224.3820357.57×7.4805≈152224.38 gallons.
Finally, we round this number to the nearest hundred. The digit in the tens place is 2 (less than 5), so we round down:
152,200\boxed{152,200}152,200 gallons.
Thus, the volume of a cylinder with radius 18 feet and depth 20 feet is approximately 152,200 gallons, making option 3 the correct choice.
