Question
Maria has a cube-shaped box that measures 9 inches along each edge. Can she fit 1,000 1-cubic-inch cubes inside the box?
A.Yes; the cube-shaped box has a volume of 1,000 cubic inches, which is equal to 1,000 cubic inches.
B.Yes; the cube-shaped box has a volume of 729 cubic inches, which is less than 1,000 cubic inches.
C.No; the cube-shaped box has a volume of 729 cubic inches, which is less than 1,000 cubic inches.
D.No; the cube-shaped box has a volume of 1,000 cubic inches, which is equal to 1,000 cubic inches.
A.Yes; the cube-shaped box has a volume of 1,000 cubic inches, which is equal to 1,000 cubic inches.
B.Yes; the cube-shaped box has a volume of 729 cubic inches, which is less than 1,000 cubic inches.
C.No; the cube-shaped box has a volume of 729 cubic inches, which is less than 1,000 cubic inches.
D.No; the cube-shaped box has a volume of 1,000 cubic inches, which is equal to 1,000 cubic inches.
Answers
GPT-4o mini
To determine whether Maria can fit 1,000 1-cubic-inch cubes inside her cube-shaped box, we first need to calculate the volume of the box.
The formula for the volume of a cube is given by:
\[
\text{Volume} = \text{side length}^3
\]
In this case, the side length of the cube-shaped box is 9 inches, so the volume is:
\[
\text{Volume} = 9^3 = 9 \times 9 \times 9 = 729 \text{ cubic inches}
\]
Next, we compare the volume of the box (729 cubic inches) to the total volume of the 1,000 1-cubic-inch cubes (which is 1,000 cubic inches).
Since 729 cubic inches is less than 1,000 cubic inches, Maria cannot fit all 1,000 cubes inside the box.
Thus, the correct answer is:
**C. No; the cube-shaped box has a volume of 729 cubic inches, which is less than 1,000 cubic inches.**
The formula for the volume of a cube is given by:
\[
\text{Volume} = \text{side length}^3
\]
In this case, the side length of the cube-shaped box is 9 inches, so the volume is:
\[
\text{Volume} = 9^3 = 9 \times 9 \times 9 = 729 \text{ cubic inches}
\]
Next, we compare the volume of the box (729 cubic inches) to the total volume of the 1,000 1-cubic-inch cubes (which is 1,000 cubic inches).
Since 729 cubic inches is less than 1,000 cubic inches, Maria cannot fit all 1,000 cubes inside the box.
Thus, the correct answer is:
**C. No; the cube-shaped box has a volume of 729 cubic inches, which is less than 1,000 cubic inches.**