The length of the rectangular parallelepiped is 90 cm, the width is 25 cm, and the height is 12 cm. Find the length of the edge of the cube, the volume of which is equal to the volume of this rectangular parallelepiped. Which of the two figures has more surface area and how much?
1. The volume of the parallelepiped:
90 x 25 x 12 = 27000 cm³.
2. The edge of the cube ∛27000 = 30 cm.
3. The area of the lateral surface of the parallelepiped:
2 x 90 x 12 + 2 x 25 x 12 + 2 x 25 x 90 = 2160 + 600 + 4500 = 7260 cm ^ 2.
4. The area of the lateral surface of the cube:
6 x 30 x 30 = 5400 cm ^ 2.
5. We calculate by how many cm ^ 2 the area of the lateral surface of the parallelepiped is larger
cube area: 7260 – 5400 = 1860 cm ^ 2.
Answer: the edge of the cube is 30 cm, the area of the lateral surface of the parallelepiped is greater than the area
cube by 1860 cm ^ 2.
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