To solve for [tex]\( h \)[/tex] in the formula for the volume of a cone [tex]\( V=\frac{1}{3} b h \)[/tex], we should isolate [tex]\( h \)[/tex] on one side of the equation. Here is a step-by-step solution:
1. Start with the given formula for the volume of a cone:
[tex]\[
V = \frac{1}{3} b h
\][/tex]
2. To eliminate the fraction on the right-hand side of the equation, multiply both sides of the equation by 3:
[tex]\[
3V = b h
\][/tex]
3. To isolate [tex]\( h \)[/tex], divide both sides of the equation by [tex]\( b \)[/tex]:
[tex]\[
h = \frac{3V}{b}
\][/tex]
Thus, the solution for [tex]\( h \)[/tex] in terms of [tex]\( V \)[/tex] and [tex]\( b \)[/tex] is:
[tex]\[
h = \frac{3V}{b}
\][/tex]
So, the correct answer is:
D. [tex]\( h = \frac{3 V}{b} \)[/tex]
