Question

1. a rectangular pyramid has a volume of 160 cubic units and a height of 6 units. what are possible dimensions for the base?

Explanation:

Step1: Recall pyramid volume formula

The volume of a rectangular pyramid is $V = \frac{1}{3} \times B \times h$, where $B$ is the area of the rectangular base, and $h$ is the height of the pyramid.

Step2: Rearrange to solve for base area

Rearrange the formula to isolate $B$: $B = \frac{3V}{h}$
Substitute $V=160$ and $h=6$:
$B = \frac{3 \times 160}{6} = 80$

Step3: Find possible base dimensions

We need pairs of positive numbers whose product is 80 (the base area).

Answer:

Possible dimensions for the base include (8 units, 10 units), (4 units, 20 units), (5 units, 16 units), or (1 unit, 80 units) (any pair of positive real numbers with a product of 80 is valid).