Question
3. square pyramid: volume \( 1,024 \mathrm{~cm}^{3} \); base edae 16 cm
Ask by Mckenzie Harper. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The height of the square pyramid is 12 cm.
Solution
Let the volume \( V \) of a square pyramid be given by
\[
V = \frac{1}{3} B h,
\]
where \( B \) is the area of the base and \( h \) is the height.
1. **Calculate the base area:**
Since the base is a square with edge length \( 16 \) cm, the area is
\[
B = 16^2 = 256 \, \mathrm{cm}^2.
\]
2. **Substitute the known values into the volume formula:**
\[
1024 = \frac{1}{3} \times 256 \times h.
\]
3. **Solve for \( h \):**
Multiply both sides by 3 to isolate \( h \) on one side:
\[
1024 \times 3 = 256h.
\]
\[
3072 = 256h.
\]
Now, divide both sides by 256:
\[
h = \frac{3072}{256} = 12 \, \mathrm{cm}.
\]
The height of the square pyramid is \( 12 \, \mathrm{cm} \).
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Simplify this solution Bonus Knowledge
To find the height of the square pyramid, you can use the formula for the volume of a pyramid: \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \). The base area of a square is the side length squared, so here it's \( 16 \, \text{cm} \times 16 \, \text{cm} = 256 \, \text{cm}^2 \). Plugging in the values, we get \( 1,024 = \frac{1}{3} \times 256 \times h \). Solving for \( h \), you find that the height is \( 12 \, \text{cm} \). Remember, when solving for height, it’s essential to double-check your calculations for errors. Also, a common mistake is not converting all measures to the same unit, which can lead to incorrect conclusions. Always keep units consistent!
