Question

The volume of one rectangular prism is 216in^3 the volume of a similiar rectangular prism is 729in^3 what is the ratio of side lengths of the two cubes?

Answer 1

plz help

Answer 2

Okay, v is l*w*h, and we know that the sides are proportional. Let's say the length of the smaller prism is l, and the larger prism is l*k where k is a constant scale factor. Because the sides are proportional, that means the larger prism is also going to have w*k and h*k as its sides. That means the volume of the little prism = l*w*h = 216 and the volume of the larger prism = l*k*w*k*h*k=729.

\[V_{small} = 216 = l*w*h\]\[V_{large}=729 = l*k*w*k*h*k=k^3*l*w*h\]Now we can substitute 216 wherever we see l*w*h in the equation for the big prism:
\[V_{large}=729=k^3*216\]
\[k^3=\frac{729}{216}=\frac{9*9*9}{6*6*6}\]
\[k=\frac{9}{6}=1.5\]
So the ratio of the sides of the big prism to those of the little prism is 1.5:1

Does that make sense?

Answer 3

Btw, I find this sort of computation to come up most frequently when deciding which size pizza to order :-) Area of a circle is proportional to the radius or diameter squared. If I have the choice of a 10" pizza for $8, or a 12" pizza for $11, which is the better deal? The ratio of the area of the big pizza is (12/10)^2:1= 1.44:1 If the price for the big pizza is less than 1.44 times the price of the small pizza, getting the bigger pizza is a better deal in terms of cost per square inch of pizza. Isn't that how everyone decides? :-) In this case, the price of the small pizza * the ratio = $8*1.44 = $11.52 which is more than the $11 the large pizza costs, so the big pizza is giving a break on the price. Next time you go out for pizza, take a look at the prices and figure out if you get a better deal by buying 1 large pizza or 2 small pizzas, and eat a slice for me!