We are asked to sketch and label in inches three different designs for a measuring cup that holds 1 cup, which is about 14.4375 cubic inches. We could make this cup be a pyramid with some sophisticated base, like below.
However, then there will be a lot of computations to find the exact dimensions of such a cup. Let's make it simple and find measuring cups in the shape of a rectangular prism. We choose this shape because the volume of a rectangular prism is equal to the product of its dimensions, but keep in mind that there are many different solutions to this problem.
Option 1
First, let the measuring cup be in the shape of a cube and s be its side length. Then its volume is V=s^3. We know that the volume of the cup has to be about 14.4375 cubic inches. Let's find s!
Therefore, the side length of the cube should be about 2.43 inches. Now, let's sketch the cube!
Option 2
Now let the measuring cup be in the shape of a square prism with a side base length of 2 inches. Let h denote its height. Then its volume is V=2* 2* h=4h. We know that the volume of the cup has to be about 14.4375 cubic inches. Let's find h!
Therefore, the height of the prism should be about 3.61 inches. Now, let's sketch the prism!
Option 3
Now let the measuring cup be in the shape of a square prism with a side base length of 3 inches. Let h denote its height. Then its volume is V=3* 3* h=9h. We know that the volume of the cup has to be about 14.4375 cubic inches. Let's find h!
