To find the height of the square pyramid, we can use the formula for the volume of a pyramid:
\[ V = \frac{1}{3} \times B \times h \]
Where:
- \( V \) is the volume of the pyramid,
- \( B \) is the area of the base,
- \( h \) is the height of the pyramid.
Since it's a square pyramid, the area of the base \( B \) can be expressed as:
\[ B = s^2 \]
where \( s \) is the length of one side of the square base.
The volume is given as \( 1980 , \text{ft}^3 \). To solve for the height \( h \), we rearrange the formula:
\[ h = \frac{3V}{B} \]
If the side length of the base \( s \) is known, we can calculate \( B \) and subsequently find \( h \). However, if you didn't provide the side length of the base, I can't calculate the height.
Assuming you refer to a side length, like \( s = 5 \) feet or \( s = 12 \) feet, we can calculate the area \( B \).
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If \( s = 5 , \text{ft} \): \[ B = 5^2 = 25 , \text{ft}^2 \] \[ h = \frac{3 \times 1980}{25} = \frac{5940}{25} = 237.6 , \text{ft} \]
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If \( s = 12 , \text{ft} \): \[ B = 12^2 = 144 , \text{ft}^2 \] \[ h = \frac{3 \times 1980}{144} = \frac{5940}{144} \approx 41.25 , \text{ft} \]
Please provide the side length \( s \) to get the correct height or specify the base area otherwise.