Questions: Solve for (h). [ V=frac13 b h ]

Solve for (h). [ V=frac13 b h ]
Transcript text: Solve for $h$. \[ V=\frac{1}{3} b h \] CHECK ANSWER
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Solution

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Solution Steps

To solve for \( h \) in the equation \( V = \frac{1}{3} b h \), we need to isolate \( h \). This can be done by multiplying both sides of the equation by 3 and then dividing by \( b \).

Step 1: Understand the Given Equation

We are given the equation for the volume of a pyramid: \[ V = \frac{1}{3} b h \] where \( V \) is the volume, \( b \) is the base area, and \( h \) is the height. We need to solve for \( h \).

Step 2: Isolate the Variable \( h \)

To solve for \( h \), we first multiply both sides of the equation by 3 to eliminate the fraction: \[ 3V = b h \] Next, divide both sides by \( b \) to isolate \( h \): \[ h = \frac{3V}{b} \]

Step 3: Substitute the Given Values

Substitute the given values \( V = 9 \) and \( b = 3 \) into the equation: \[ h = \frac{3 \times 9}{3} \]

Step 4: Calculate the Value of \( h \)

Perform the calculation: \[ h = \frac{27}{3} = 9.0 \]

Final Answer

\[ \boxed{h = \frac{3V}{b}} \]

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