What is the volume of a cone with height 1 ft and diameter 2 ft? Use π ≈ 3.14 and round your answer to the nearest hundredth.
Understand the Problem
The question is to calculate the volume of a cone, given its height and diameter. We will use the formula for the volume of a cone, which is V = (1/3) * π * r^2 * h, where r is the radius and h is the height. We are given that π ≈ 3.14, height h = 1 ft, and diameter = 2 ft, so the radius r = 1 ft.
Answer
$1.05$
Answer for screen readers
$1.05$
Steps to Solve
- Find the radius
The diameter is given as 2 ft, so the radius $r$ is half of the diameter: $r = \frac{2}{2} = 1$ ft
- Apply the formula
The volume $V$ of a cone is given by the formula $V = \frac{1}{3} \pi r^2 h$. We are given that $h = 1$ ft and $r = 1$ ft. Using $\pi \approx 3.14$, we can calculate the volume:
$V = \frac{1}{3} \times 3.14 \times (1)^2 \times 1$
- Calculate the volume
Simplify the expression to find the value of $V$:
$V = \frac{1}{3} \times 3.14 \times 1 \times 1 = \frac{3.14}{3}$
$V = 1.04666...$
- Round to the nearest hundredth
Round the volume to the nearest hundredth:
$V \approx 1.05$ cubic feet
$1.05$
More Information
The volume of the cone is approximately 1.05 cubic feet. The units are cubic feet because we are dealing with volume, which is a three-dimensional measure.
Tips
A common mistake is forgetting to divide the diameter by 2 to find the radius. Also, rounding errors can occur if the calculation isn't precise enough before rounding to the nearest hundredth at the end. Make sure to use the correct formula for the volume of a cone.
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