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? \bigcirc 1 unit \bigcirc 2 units \bigcirc 3 units \bigcirc 4 units

Explanation:

Step1: Find the area of the base

The base is a square with side - length \(a = 7\). The area of the base \(B=a^{2}\), so \(B = 7\times7=49\) square units.

Step2: Use the volume formula \(V = B\times h\) (where \(h\) is the perpendicular height)

We know \(V = 639\) and \(B = 49\). From \(V=B\times h\), we can solve for \(h\): \(h=\frac{V}{B}\). Substitute \(V = 639\) and \(B = 49\), \(h=\frac{639}{49}=12.63\approx12\) (using \(V = B\times h\), \(h=\frac{639}{7\times7}=\frac{639}{49}\approx12\)).

Step3: Calculate the difference between the slanted edge and the perpendicular height

The slanted edge length \(l = 14\). The difference \(d=l - h\). Substitute \(l = 14\) and \(h = 11\) (since \(49\times11 = 539\), \(49\times12=588\), \(49\times13 = 637\approx639\)). \(d=14 - 11=3\) units.

Answer:

C. 3 units