Question

select the correct answer. three cube - shaped boxes are stacked one above the other. the volumes of two of the boxes are 1,331 cubic meters each, and the volume of the third box is 729 cubic meters. what is the height of the stacked boxes in meters? a. 19 b. 29 c. 30 d. 31

Explanation:

Step1: Find side length of first two cubes

The volume of a cube is given by \( V = s^3 \), where \( s \) is the side length. For the cubes with volume \( 1331 \, \text{m}^3 \), we solve \( s^3 = 1331 \). Taking the cube root, \( s=\sqrt[3]{1331}=11 \, \text{m} \) (since \( 11\times11\times11 = 1331 \)).

Step2: Find side length of the third cube

For the cube with volume \( 729 \, \text{m}^3 \), solve \( s^3 = 729 \). Taking the cube root, \( s=\sqrt[3]{729}=9 \, \text{m} \) (since \( 9\times9\times9 = 729 \)).

Step3: Calculate total height of stacked cubes

There are two cubes with side length \( 11 \, \text{m} \) and one with side length \( 9 \, \text{m} \). The total height is \( 11 + 11 + 9 = 31 \, \text{m} \)? Wait, no, wait. Wait, the problem says "three cube - shaped boxes are stacked one above the other. The volumes of two of the boxes are 1,331 cubic meters each, and the volume of the third box is 729 cubic meters." Wait, no, maybe I misread. Wait, 1331 cube root is 11, 729 cube root is 9. So two boxes of side 11 and one of side 9. So total height is \( 11 + 11+9=31 \)? But wait, let's check again. Wait, 111111 = 1331, 999 = 729. So two 11s and one 9: 11 + 11+9 = 31. But wait, the options are A.19, B.29, C.30, D.31. So D is 31. Wait, but let me check my calculation again. Wait, maybe I made a mistake. Wait, 1331 is 11³, 729 is 9³. So two cubes of side 11 and one of side 9. So height is 11 + 11+9 = 31. So the answer should be D.

Answer:

D. 31