an oblique rectangular prism with a square base has a volume of 539 cubic units. the edges of the prism…
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
Answer
Explanation:
Step1: Find the base - area of the prism
The base is a square with side - length $a = 7$ units. The base - area $B$ of a square is given by $B=a^{2}$. So, $B = 7^{2}=49$ square units.
Step2: Find the perpendicular height $h$ of the prism
The volume $V$ of a prism is given by $V = Bh$. We know that $V = 539$ cubic units and $B = 49$ square units. Rearranging the formula for $h$, we get $h=\frac{V}{B}$. Substituting the values, $h=\frac{539}{49}=11$ units.
Step3: Find the difference between the slanted edge length and the perpendicular height
The slanted edge length is 14 units and the perpendicular height $h = 11$ units. The difference $d$ is $d=14 - 11=3$ units.
Answer:
3 units