What is the volume, in cubic ft, of a cylinder with a height of 3ft and a base radius of 4ft, to the nearest tenths place?
The correct answer and explanation is:
Correct Answer: 150.8 cubic feet
To find the volume of a cylinder, use the formula: V=πr2hV = \pi r^2 h
Where:
- VV is the volume
- rr is the radius of the base
- hh is the height
- π\pi is approximately 3.1416
Given:
- Radius r=4r = 4 feet
- Height h=3h = 3 feet
Step 1: Square the radius r2=42=16r^2 = 4^2 = 16
Step 2: Multiply by the height 16×3=4816 \times 3 = 48
Step 3: Multiply by π\pi 48×3.1416=150.796848 \times 3.1416 = 150.7968
Step 4: Round to the nearest tenth 150.7968≈150.8150.7968 \approx 150.8
So, the volume is 150.8 cubic feet.
This result represents the amount of three-dimensional space inside the cylinder. The base of the cylinder is a circle, and the formula for the area of a circle is πr2\pi r^2. That area is multiplied by the height to get the volume of the entire cylinder.
The reason for using π\pi is that circular shapes are involved, and π\pi defines the relationship between a circle’s diameter and its circumference. By including π\pi in the volume formula, the calculation accounts for the circular shape of the base.
This formula is derived from basic principles of geometry. A cylinder can be thought of as a stack of identical circular disks placed one on top of the other. The area of each disk is πr2\pi r^2, and stacking them to a height of hh gives the volume.
This kind of calculation is useful in real-world applications like measuring storage tanks, pipes, and barrels. Using accurate values and correct rounding ensures reliable results in construction, manufacturing, and engineering.