Question

1. what is the volume of a cone, in cubic feet, with a height of 1 foot and a radius of $\frac{1}{4}$ foot? (2004 - 2005 math is cool, question #39) a. $\frac{1}{48}pimathrm{ft}^3$ b. $\frac{1}{16}pimathrm{ft}^3$ c. $\frac{1}{12}pimathrm{ft}^3$ d. $\frac{1}{4}pimathrm{ft}^3$ $v_{\theta}=\frac{1}{3}pi r^{2}h$

Explanation:

Step1: Identify the formula

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$.

Step2: Substitute the values

Given $h = 1$ foot and $r=\frac{1}{4}$ foot. Substitute into the formula: $V=\frac{1}{3}\pi(\frac{1}{4})^{2}\times1$.

Step3: Calculate $(\frac{1}{4})^{2}$

$(\frac{1}{4})^{2}=\frac{1}{4}\times\frac{1}{4}=\frac{1}{16}$.

Step4: Calculate the volume

$V=\frac{1}{3}\pi\times\frac{1}{16}\times1=\frac{1}{48}\pi$ cubic - feet.

Answer:

A. $\frac{1}{48}\pi\ ft^{3}$