Multiple choice

John built a rectangular cardboard box $25$ cm high with a square base and a volume of $2,500$ $\displaystyle { cm }^{ 3 }$. Then he realized he did not need a box that large, so he chopped off the height of the box reducing its volume to $1,000$ $\displaystyle { cm }^{ 3 }$. Was the new box cubical? Also, state its' height.

  1. $20cm$
  2. $10cm$
  3. $30cm$
  4. $40cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original box: Base area * height = 2500. Base area * 25 = 2500, so base area = 100. Since the base is square, side = 10. New box: Volume = 1000, Base area = 100 (remains the same). Height = 1000 / 100 = 10. Since height = side = 10, the new box is cubical.

AI explanation

The original square base has an area found by dividing the volume of 2500 by the height of 25, which gives 100 square cm, meaning the base side lengths are 10 cm each. Reducing the volume to 1000 cubic cm while keeping the 10 cm by 10 cm base means the new height is 1000 divided by 100. The new height is 10 cm, and since all three dimensions (10 cm by 10 cm by 10 cm) are equal, the new box is cubical.

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