Calculating height of cone given volume and radius
The volume of a cone is given by the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height of the cone. Here, we are given:
\[ V = 37.68 \, \text{cubic centimeters} \]
\[ r = 3 \, \text{centimeters} \]
\[ \pi \approx 3.14 \]
Let's solve for \( h \):
\[ 37.68 = \frac{1}{3} \times 3.14 \times 3^2 \times h \]
\[ 37.68 = \frac{1}{3} \times 3.14 \times 9 \times h \]
\[ 37.68 = 3.14 \times 3 \times h \]
\[ 37.68 = 9.42 \times h \]
\[ h = \frac{37.68}{9.42} \]
\[ h \approx 4 \]
Rounding to the nearest hundredth, \( h \) would then be \( 4.00 \) centimeters.
