A pyramid has a square base. The side of square is 12 cm and height of pyramid is 21 cm. The pyramid is cut into 3 parts by 2 cuts parallel to its base. The cuts are at height of 7 cm and 14 cm respectively from the base. What is the difference (in cm3) in the volume of top most and bottom most part?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 672cm3
Height of each part = 7 cm
Ratio of height of three pyramids = 1 : 2 : 3
Length of bases of pyramids are 4 cm, 8 cm and 12 cm
Volume of top part = 1/3 × 42 × 7 = 112/3 cm3
Volume of bottom part = 1/3[122 × 21 - 82×14] = 2128/3
Required difference = 2128/3 - 112/3 = 2016/3 = 672 cm3