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If you shorten the height of a cuboid by 3cm, it will become a cube. The surface area will be reduced by 72cm2. What is the volume of the cuboid?
72 △ 3 = 24 cm (this is the circumference of the bottom of the cuboid)
So, the side length of the bottom of the cuboid is 6cm (the bottom is a square)
Height of cuboid = 6 + 3 = 9 cm
Cuboid volume = 6 * 6 * 9 = 324 (cm3)
If the height of a cuboid is increased by 3 cm, it will become a cube. At this time, the surface area is increased by 96 square cm. What is the volume of the original cuboid?
The area of one additional face: 96 △ 4 = 24 (square centimeter); the length (width) of the cuboid: 24 △ 3 = 8 (centimeter); the height of the cuboid: 8-3 = 5 (centimeter); the volume: 8 × 8 × 5 = 320 (cubic centimeter); a: the volume of the cuboid is 320 cubic centimeter
Reduce the length of a cuboid by 2 cm to become a cube,
The surface area of the cube is 24 square centimeters less than that of the cuboid
The perimeter of the bottom surface is 24 △ 2 = 12 cm
So the bottom side length is 12 △ 4 = 3cm
Length 3 + 2 = 5cm
therefore
Surface area (3 × 5 + 3 × 5 + 3 × 3) × 2 = 78 square centimeter
Volume 3 × 3 × 5 = 45 CC
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