Question

rectangular pyramids x and y have equal volumes. which is the height, h, of pyramid y? a. 17 cm b. 20 cm c. 23 cm d. 26 cm

Explanation:

Step1: Recall volume formula for rectangular pyramid

The volume formula for a rectangular pyramid is $V=\frac{1}{3}lwh$, where $l$ is the length of the base, $w$ is the width of the base and $h$ is the height. For pyramid $X$, $l = 13$ cm, $w=12$ cm and $h = 20$ cm. So $V_X=\frac{1}{3}\times13\times12\times20$.

Step2: Calculate volume of pyramid X

$V_X=\frac{1}{3}\times13\times12\times20=13\times4\times20 = 1040$ $cm^3$.

Step3: Set up volume - equation for pyramid Y

For pyramid $Y$, $l = 12$ cm, $w = 10$ cm and height is $h$. Since $V_X = V_Y$, we have $\frac{1}{3}\times12\times10\times h=1040$.

Step4: Solve for h

First, simplify the left - hand side of the equation: $\frac{1}{3}\times12\times10\times h = 4\times10\times h=40h$. Then, solve the equation $40h = 1040$ for $h$. Divide both sides by 40: $h=\frac{1040}{40}=26$ cm.

Answer:

D. 26 cm