The volume of a larger prism is 168 cubic cm. if the prisms are similar with a linear ratio of 3:2 what is the volume of the smaller prism?
How do i figure that out?
Did you learn that the volumes of similar objects are proportional to the cubes of their sides?
so vol(smaller prism)/168 = (3^3)/(2^3)
etc.
To figure out the volume of the smaller prism, you can use the concept that the volumes of similar objects are proportional to the cubes of their sides.
First, write down the given information. We know that the volume of the larger prism is 168 cubic cm. We also know that the linear ratio between the larger and smaller prisms is 3:2.
Next, set up an equation using the volume ratios of the two prisms:
(volume of smaller prism) / 168 = (3^3) / (2^3)
Here, we cube each side of the ratio because we're comparing volumes, which are three-dimensional.
Now, you can solve for the volume of the smaller prism by rearranging the equation:
(volume of smaller prism) = (3^3) / (2^3) * 168
Calculate the numerator:
(3^3) = 27
Calculate the denominator:
(2^3) = 8
Next, multiply the numerator and denominator:
(27 / 8) * 168
Finally, perform the multiplication to find the volume of the smaller prism:
(volume of smaller prism) ≈ 567 cubic cm
Therefore, the volume of the smaller prism is approximately 567 cubic cm.