Question

question 1
given that the volume of the square pyramid is 256 mm³, find the height. round answer to two decimal places.
height = mm³

Explanation:

Step1: Recall Volume Formula for Square Pyramid

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. For a square base with side length \( s \), \( B = s^2 \). Here, \( s = 8 \) mm, so \( B = 8^2 = 64 \) \( \text{mm}^2 \).

Step2: Substitute Known Values into Formula

We know \( V = 256 \) \( \text{mm}^3 \) and \( B = 64 \) \( \text{mm}^2 \). Substitute into \( V = \frac{1}{3}Bh \):
\( 256 = \frac{1}{3} \times 64 \times h \)

Step3: Solve for \( h \)

First, simplify the right - hand side: \( \frac{1}{3} \times 64\times h=\frac{64h}{3} \).
Then, multiply both sides by 3 to get rid of the fraction: \( 256\times3 = 64h \).
\( 768 = 64h \).
Now, divide both sides by 64: \( h=\frac{768}{64}=12.00 \) (since \( 768\div64 = 12 \)).

Answer:

\( 12.00 \)