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. $h=\frac{3}{vs^{2}}$ part b what is the height of a square pyramid with volume $v = 400$ cm³ and side length $s = 10$ cm? height: cm

Explanation:

Step1: Isolate h in volume formula

Given $V=\frac{1}{3}s^{2}h$, multiply both sides by 3 to get $3V = s^{2}h$.

Step2: Solve for h

Divide both sides of $3V = s^{2}h$ by $s^{2}$, we have $h=\frac{3V}{s^{2}}$. So the answer for Part A is A.

Step3: Substitute values for Part B

Substitute $V = 400$ and $s = 10$ into $h=\frac{3V}{s^{2}}$. Then $h=\frac{3\times400}{10^{2}}$.

Step4: Calculate the value of h

First, calculate $10^{2}=100$ and $3\times400 = 1200$. Then $h=\frac{1200}{100}=12$.

Answer:

Part A: A. $h=\frac{3V}{s^{2}}$
Part B: 12