What is the volume, in cubic ft, of a cylinder with a height of 15 ft and a base radius of 10 ft, to the nearest tenths place?
The correct answer and explanation is:
Correct Answer:
The volume of the cylinder is 4712.4 cubic feet (to the nearest tenth).
Explanation:
To find the volume of a cylinder, the standard formula is: V=πr2hV = \pi r^2 h
Where:
- VV is the volume
- π≈3.1416\pi \approx 3.1416
- rr is the radius of the circular base
- hh is the height of the cylinder
In this case:
- Radius r=10r = 10 feet
- Height h=15h = 15 feet
Now, substitute the values into the formula: V=3.1416×(10)2×15V = 3.1416 \times (10)^2 \times 15 V=3.1416×100×15V = 3.1416 \times 100 \times 15 V=3.1416×1500V = 3.1416 \times 1500 V=4712.4 cubic feetV = 4712.4 \text{ cubic feet}
The result is rounded to the nearest tenth as requested.
The concept behind this formula is based on how the volume of a prism is calculated. A cylinder is essentially a circular prism. Its volume is determined by taking the area of the base and multiplying it by the height. The base is a circle, so its area is πr2\pi r^2. The height tells how far that area extends vertically, which gives the total space the cylinder occupies.
This formula is applicable for all right circular cylinders. The units remain in cubic feet because the radius and height are in feet, and area multiplied by height gives volume. This kind of calculation is common in real-life applications such as determining the capacity of tanks, silos, and pipes. Precision to the nearest tenth is important when estimating physical quantities in engineering and construction projects.