QuestionJuly 26, 2025

Select the correct answer from each drop-down menu. Acubo shaped box has a side length of 15 inches and contains 27 identical cube shaped blocks. What is the surface area of all 27 blocks compared to the surface area of the box? The side length of the blocks is square inches, so the total surface area of the 27 blocks is square square inches. This is square the surface area of the box

Select the correct answer from each drop-down menu. Acubo shaped box has a side length of 15 inches and contains 27 identical cube shaped blocks. What is the surface area of all 27 blocks compared to the surface area of the box? The side length of the blocks is square inches, so the total surface area of the 27 blocks is square square inches. This is square the surface area of the box
Select the correct answer from each drop-down menu.
Acubo shaped box has a side length of 15 inches and contains 27 identical cube shaped blocks. What is the surface area of all 27 blocks compared
to the surface area of the box?
The side length of the blocks is square  inches, so the total surface area of the 27 blocks is square  square inches. This is
square  the surface area of the box

Solution
4.6(190 votes)

Answer

The side length of the blocks is 5 inches, so the total surface area of the 27 blocks is 4050 square inches. This is 3 times the surface area of the box. Explanation 1. Calculate the side length of each block The volume of the box is 15^3 = 3375 cubic inches. Each block has a volume of \frac{3375}{27} = 125 cubic inches. Therefore, the side length of each block is \sqrt[3]{125} = 5 inches. 2. Calculate the surface area of one block Surface area of one block is 6 \times (5^2) = 150 square inches. 3. Calculate the total surface area of all blocks Total surface area of 27 blocks is 27 \times 150 = 4050 square inches. 4. Calculate the surface area of the box Surface area of the box is 6 \times (15^2) = 1350 square inches. 5. Compare the surface areas The total surface area of the blocks is \frac{4050}{1350} = 3 times the surface area of the box.

Explanation

1. Calculate the side length of each block<br /> The volume of the box is $15^3 = 3375$ cubic inches. Each block has a volume of $\frac{3375}{27} = 125$ cubic inches. Therefore, the side length of each block is $\sqrt[3]{125} = 5$ inches.<br /><br />2. Calculate the surface area of one block<br /> Surface area of one block is $6 \times (5^2) = 150$ square inches.<br /><br />3. Calculate the total surface area of all blocks<br /> Total surface area of 27 blocks is $27 \times 150 = 4050$ square inches.<br /><br />4. Calculate the surface area of the box<br /> Surface area of the box is $6 \times (15^2) = 1350$ square inches.<br /><br />5. Compare the surface areas<br /> The total surface area of the blocks is $\frac{4050}{1350} = 3$ times the surface area of the box.
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