Xenia wants to stuff a cube-shaped footstool that measures 10.25 inches on all edges. What is a good estimate of the number of cubic inches of foam peanuts that she will need?
a. just over 1,331 cubic inches
b. just over 1,000 cubic inches
c. just over 30 cubic inches
d. just over 33 cubic inches
since 10.25 is just over 10,
and 10^3 = 1000, I'd say (b)
To find the estimate of the number of cubic inches of foam peanuts that Xenia will need, we need to find the volume of the cube-shaped footstool. The volume of a cube is calculated by multiplying the length of one side by itself three times (since a cube has three equal sides).
In this case, the length of one side of the cube is given as 10.25 inches. Therefore, the volume of the cube can be calculated as follows:
Volume = (Length of side)³
Volume = 10.25³
Using a calculator, we find:
Volume = 1071.515625 cubic inches
Now, let's look at the answer choices:
a. just over 1,331 cubic inches
b. just over 1,000 cubic inches
c. just over 30 cubic inches
d. just over 33 cubic inches
The closest estimate to the actual volume of 1071.515625 cubic inches is option b. just over 1,000 cubic inches. Therefore, the correct answer is option b. just over 1,000 cubic inches.