Question

the formula for the volume of a square pyramid is v = \frac{1}{3}s^{2}h.
part a
which formula gives the height h of the square pyramid in terms of s and v?
a. h = \frac{3v}{s^{2}}
b. h = \frac{3s}{v^{2}}
c. h = \frac{s^{2}}{3v}
d. h = \frac{3}{v^{2}}
part b
what is the height of a square pyramid with volume v = 400 cm³ and side length s = 10 cm?
height 12 cm

Explanation:

Step1: Recall the volume formula

The volume formula for a square pyramid is \( V=\frac{1}{3}s^{2}h \).

Step2: Solve for \( h \)

Multiply both sides of the formula \( V = \frac{1}{3}s^{2}h \) by \( 3 \) to get \( 3V=s^{2}h \). Then divide both sides by \( s^{2} \), so \( h=\frac{3V}{s^{2}} \).

Step3: Substitute values for Part B

Given \( V = 400\mathrm{cm}^{3}\) and \( s = 10\mathrm{cm}\). Substitute into \( h=\frac{3V}{s^{2}}\), we have \( h=\frac{3\times400}{10^{2}}=\frac{1200}{100}=12\mathrm{cm}\)

Answer:

For Part A: A. \( h=\frac{3V}{s^{2}}\)
For Part B: \( 12\mathrm{cm}\)