Question

an oblique rectangular prism with a square base has a volume of 539 cubic units. the edges of the prism measure 7 by 7 by 14 units. how many units longer is the slanted edge length of the prism, 14, compared to its perpendicular height? 1 unit 2 units 3 units 4 units

Explanation:

Step1: Calculate the base - area

The base is a square with side length $a = 7$ units. The area of the base $B=a^{2}=7^{2}=49$ square units.

Step2: Find the perpendicular height

The volume formula of a prism is $V = B\times h$, where $V$ is volume, $B$ is base - area and $h$ is perpendicular height. Given $V = 539$ cubic units and $B = 49$ square units. We can solve for $h$: $h=\frac{V}{B}=\frac{539}{49}=11$ units.

Step3: Calculate the difference

The slanted edge length is 14 units and the perpendicular height is 11 units. The difference is $14 - 11=3$ units.

Answer:

3 units