Question

Write a function to model the situation.

a box is w inches wide. the box is twice as long as it is wide and 3.5 times as tall as it is wide. write a function to model the volume (v) of the box in cubic inches as a function of its width.

please help and thank you!​

Answer 1

v(w) = 7w³

Explanation:

The formula for the volume of a cuboid (rectangular prism, or box) is ...

V = LWH . . . . . . where L represent length, W represents width, and H represents height

The problem statement tells you that for a box of width w (in inches), the length is 2w, and the height is 3.5w. Using these values in the formula, we have ...

V = (2w)(w)(3.5w)

V = 7w³

Written as a function v(w), volume as a function of width, this is ...

v(w) = 7w³