A regular right pyramid with an equilateral triangular base of side 18 cm is completely submerged in a cylindrical tank of radius 10 cm, initially filled with water to a height of 25 cm. The pyramid's apex just touches the bottom of the tank. Given that the water level in the tank rises to 28 cm after the pyramid is submerged, find the perpendicular height of the pyramid.
Show answer & explanation
Correct answer: C
Explanation
Given:
Radius of cylinder = 10 cm
Initial water level = 25 cm
Final water level = 28 cm
Side of equilateral triangle = 18 cm
By formula:
Volume = base area × height
Rise in water level = 28 − 25 = 3 cm
Volume of cylinder (displaced) = πr²h
= π × 10² × 3 = 300π
Now volume of pyramid = (1/3) × base area × height
Area of equilateral triangle = (√3 / 4) × a² = 81√3
(1/3) × 81√3 × h = 300π
27√3 h = 300π
h = 300π / (27√3)
h = 20.14 cm