A rectangular box contains 199 cubic inches. If a similar box has the same length but double the height and triple the width, how many cubic inches does this box contain?

Work Shown:

r = 7 is the radius

h = 4 is the height

V = volume of cone

V = (1/3)*pi*r^2*h

V = (1/3)*pi*7^2*4

V = (1/3)*pi*49*4

V = (1/3)*pi*196

V = (1/3)*196*pi

V = (196/3)*pi

The units are in cubic inches. Think of a box that is 1 inch by 1 inch by 1 inch. The volume of that box would be (1inch)*(1inch)*(1inch) = (1*1*1) (inch*inch*inch) = 1 inch^3 = 1 cubic inch.

We can write "cubic inch" as "in^3".