Question

4b: what error was made in student bs work? (worth 2 points) *
student b:
$v=\frac{1}{3}bh$
$v = \frac{1}{3}(12\times12)(10)$
$v=\frac{1}{3}(144)(10)$
$v=(48)(10)$
$v = 480 in^{3}$
your answer

4c: set up the correct equation to solve for the volume of the square pyramid, and substitute in the correct variables. (worth 2 point)
your answer

4d: what is the correct volume of the square pyramid? (worth 2 points) *
your answer

Explanation:

Step1: Analyze student B's work

The formula for the volume of a square - pyramid is $V=\frac{1}{3}Bh$, where $B$ is the area of the base and $h$ is the height. Student B correctly identified $B = 12\times12 = 144$ and $h = 10$. But when calculating $\frac{1}{3}(144)(10)$, the error is in the first - step of the multiplication.

Step2: Correct the calculation

The correct way to calculate $\frac{1}{3}(144)(10)$ is first $\frac{144}{3}=48$, then $48\times10 = 480$. But the error in student B's work is that they divided only the first factor of the product $(144)(10)$ by 3 instead of dividing the whole product $144\times10$ by 3 at once. The correct calculation should be $\frac{1}{3}\times(144\times10)=\frac{1440}{3}=480$.

Step3: Set up the correct equation

The volume formula for a square - pyramid with base side length $s = 12$ and height $h = 10$ is $V=\frac{1}{3}s^{2}h$. Substituting $s = 12$ and $h = 10$, we get $V=\frac{1}{3}(12^{2})(10)=\frac{1}{3}(144)(10)$.

Step4: Calculate the correct volume

$V=\frac{1}{3}(144)(10)=\frac{144\times10}{3}=\frac{1440}{3}=480$ in³.

Answer:

4B: The error is dividing only the first factor of the product $(144)(10)$ by 3 instead of dividing the whole product $144\times10$ by 3 at once.
4C: $V=\frac{1}{3}(12^{2})(10)$
4D: $480$ in³