Question

question 10 (multiple choice worth 1 points) (05.02 mc) a square pyramid has a height of 6 units and a volume of 70 units³. if a square prism has the same base area and volume as the square pyramid, what is its height? o 2 units o 4 units o 6 units o 8 units

Explanation:

Step1: Recall volume formulas

The volume formula for a square - pyramid is $V_{pyramid}=\frac{1}{3}Bh$, where $B$ is the base area and $h$ is the height. The volume formula for a square - prism is $V_{prism}=Bh$, where $B$ is the base area and $h$ is the height.
We know that $V_{pyramid} = 70$ units³ and $h_{pyramid}=6$ units. Using the pyramid volume formula $V_{pyramid}=\frac{1}{3}Bh$, we can find the base area $B$.
$70=\frac{1}{3}B\times6$.

Step2: Solve for base area $B$

First, simplify the right - hand side of the equation $70=\frac{1}{3}B\times6$. Since $\frac{1}{3}\times6 = 2$, the equation becomes $70 = 2B$.
Then, solve for $B$ by dividing both sides of the equation by 2: $B=\frac{70}{2}=35$ square units.

Step3: Use prism volume formula

Since the square prism has the same volume $V_{prism}=70$ units³ and the same base area $B = 35$ square units, and using the prism volume formula $V_{prism}=Bh_{prism}$.
We substitute $V_{prism}=70$ and $B = 35$ into the formula: $70=35h_{prism}$.

Step4: Solve for prism height $h_{prism}$

Divide both sides of the equation $70 = 35h_{prism}$ by 35: $h_{prism}=\frac{70}{35}=2$ units.

Answer:

2 units