Question

find the volume of a road construction marker, a cone with height 2 ft and base radius 1/2 ft. use 3.14 as an approximation for π. the volume of the cone is (simplify your answer. type an (round to the nearest hundredth as needed.)

Explanation:

Step1: Recall volume - formula for a cone

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$, where $r$ is the radius of the base and $h$ is the height of the cone.

Step2: Substitute given values

We are given that $r = \frac{1}{2}$ ft and $h = 2$ ft, and $\pi\approx3.14$. Substitute these values into the formula: $V=\frac{1}{3}\times3.14\times(\frac{1}{2})^{2}\times2$.

Step3: Simplify the expression

First, calculate $(\frac{1}{2})^{2}=\frac{1}{4}$. Then the expression becomes $V=\frac{1}{3}\times3.14\times\frac{1}{4}\times2$. Multiply the numbers: $3.14\times\frac{1}{4}\times2=\frac{3.14\times2}{4}=1.57$. Then $V = \frac{1}{3}\times1.57$.
$V=\frac{1.57}{3}\approx0.52$ $ft^{3}$.

Answer:

$0.52$ $ft^{3}$