Question - Calculating height of cone given volume and radius
Solution:
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.
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