Multiple choice

A square pyramid is inscribed in a cube of total surface area of $24$ square cm such that the base of the pyramid is the same as the base of the cube. What is the volume of the pyramid?

  1. $\dfrac 13$
  2. $\dfrac 83$
  3. $6$
  4. $4$
  5. $8$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The series follows the pattern 3^1, 3^2, 3^3, 3^4, 3^5. The missing term is 3^4 = 81.

AI explanation

The total surface area of the cube is 6 * s^2 = 24, so the side length s is 2 cm. The volume of the pyramid is one-third the volume of the cube when they share the same base and height, using the formula V = (1/3) * base_area * height. Therefore, the pyramid's volume is (1/3) * (2 * 2) * 2 = 8/3 cubic cm.

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