A rectangular prism has a volume of 54 cubic centimeters. If the length, width, and height are all changed to 1/3 of their original size, what will be the volume of the new rectangular prism?

lwh = 52

new dimensions: l/3, w/3, h/3
new volume = (l/3)(w/3)(h/3) = lwh/27 = 52/27
so it is (1/27) of the original

Find the volume of a rectangular prism with l= 15 in., w=13 in., and h= 8 in.

Objection! Clearly you do not have the ability to solve this problem, hence you are posting it in an education forum! Take that!

22 of corse

To find the volume of the new rectangular prism, we need to understand the relationship between the volumes of similar shapes.

When one dimension of a shape is multiplied by a certain factor, the volume is multiplied by the cube of that factor (since there are three dimensions involved). This is because changing the scale of the shape affects all three dimensions equally.

In this case, the length, width, and height of the rectangular prism are being changed to 1/3 of their original size. This means they are being multiplied by a factor of 1/3.

To find the volume of the new rectangular prism, we can calculate:

Volume of the new rectangular prism = (1/3)^3 * volume of the original rectangular prism

Given that the volume of the original rectangular prism is 54 cubic centimeters:

Volume of the new rectangular prism = (1/3)^3 * 54

Simplifying this expression:

Volume of the new rectangular prism = (1/27) * 54

Volume of the new rectangular prism = 2 cubic centimeters

Therefore, the volume of the new rectangular prism will be 2 cubic centimeters.