Question

given that the volume of the square pyramid is 234.67 m³, find the height. round answer to two decimal places.
8 m
8 m
height =
m³

Explanation:

Step1: Recall Volume Formula

The volume \( V \) of a square pyramid is given by \( V = \frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height. The base is a square with side length \( 8 \, \text{m} \), so \( B = 8 \times 8 = 64 \, \text{m}^2 \).

Step2: Substitute Values and Solve for \( h \)

We know \( V = 234.67 \, \text{m}^3 \) and \( B = 64 \, \text{m}^2 \). Substitute into the formula:
\( 234.67 = \frac{1}{3} \times 64 \times h \)
First, multiply both sides by \( 3 \): \( 234.67 \times 3 = 64h \)
\( 704.01 = 64h \)
Then, divide both sides by \( 64 \): \( h = \frac{704.01}{64} \approx 11.00 \) (rounded to two decimal places). Wait, let's recalculate: \( 704.01 \div 64 = 11.00015625 \), so approximately \( 11.00 \)? Wait, no, wait: \( 234.67 \times 3 = 704.01 \), then \( 704.01 \div 64 \). Let's do the division: 6411 = 704, so 704.01 - 704 = 0.01, so 11 + 0.01/64 ≈ 11.000156, so to two decimal places, 11.00? Wait, maybe I made a mistake. Wait, the volume formula: \( V = \frac{1}{3}s^2h \), where \( s \) is the side of the square base. So \( s = 8 \), so \( s^2 = 64 \). So \( 234.67 = \frac{1}{3} \times 64 \times h \). So \( h = \frac{234.67 \times 3}{64} \). Let's compute 234.673: 2343=702, 0.673=2.01, so total 704.01. Then 704.01 / 64: 6411 = 704, so 704.01 - 704 = 0.01, so 11 + 0.01/64 = 11.00015625, so rounded to two decimal places, 11.00? Wait, but maybe the calculation is 234.673=704.01, 704.01/64=11.00015625, so yes, 11.00 when rounded to two decimal places. Wait, but let me check again. Wait, 64*11=704, so 704.01 is 0.01 more than 704, so 11.000156, so two decimal places is 11.00.

Answer:

\( 11.00 \)