Calculating Cone Radius With Given Volume and Height
To find the radius of the cone, we can use the formula for the volume of a cone:
\[ V = \frac{1}{3}\pi r^2 h \]
Where:
- \( V \) is the volume of the cone,
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone,
- \( \pi \) is approximately 3.14 (given).
The volume (\( V \)) is given as 37.68 cubic millimeters, and the height (\( h \)) is given as 4 millimeters. To find \( r \), we can rearrange the formula to solve for \( r^2 \):
\[ r^2 = \frac{3V}{\pi h} \]
Now we'll use the given values:
\[ r^2 = \frac{3 \times 37.68}{3.14 \times 4} \]
First, let's calculate the numerator of the fraction:
\[ 3 \times 37.68 = 113.04 \]
And the denominator of the fraction:
\[ 3.14 \times 4 = 12.56 \]
Next, we'll divide these two results to find \( r^2 \):
\[ r^2 = \frac{113.04}{12.56} \approx 9 \]
Now take the square root of 9 to find the radius \( r \):
\[ r = \sqrt{9} = 3 \]
So the radius \( r \) of the cone is 3 millimeters. Since the problem asks to round our answer to the nearest hundredth, our final answer in two decimal places would still be:
\[ r \approx 3.00 \text{ millimeters} \]
