A certain physical quantity is calcualted from the formula `(pi)/(3)(a^(2)-b^(2))` h where h, a and b are all lengths. The quantity being calculated is

Options

A. velocity
B. length
C. area
D. volume

Answer

To solve the problem, we need to analyze the given formula and determine the physical quantity it represents. The formula provided is:

\[ x = \frac{\pi}{3} (a^2 - b^2) h \]

where \( h \), \( a \), and \( b \) are all lengths.

### Step 1: Identify the dimensions of the terms in the formula
- Since \( h \), \( a \), and \( b \) are lengths, their dimensions can be represented as:
- \( [h] = L \)
- \( [a] = L \)
- \( [b] = L \)

### Step 2: Analyze the expression \( a^2 - b^2 \)
- The term \( a^2 - b^2 \) involves squaring the lengths:
- \( [a^2] = L^2 \)
- \( [b^2] = L^2 \)
- Therefore, \( [a^2 - b^2] = L^2 \) (since both terms have the same dimensions, the subtraction does not change the dimension).

### Step 3: Combine the dimensions in the formula
- Now, substituting back into the formula:
\[ x = \frac{\pi}{3} (a^2 - b^2) h \]
- The dimensions of \( x \) can be determined as follows:
\[ [x] = [\frac{\pi}{3}] \cdot [a^2 - b^2] \cdot [h] \]
- Since \( \frac{\pi}{3} \) is a constant (dimensionless), we have:
\[ [x] = L^2 \cdot L = L^3 \]

### Step 4: Interpret the result
- The dimension \( L^3 \) corresponds to the volume of a three-dimensional object.

### Conclusion
The quantity being calculated by the formula \( \frac{\pi}{3} (a^2 - b^2) h \) is **volume**.

### Final Answer
The quantity being calculated is **volume**.

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