A solid is in the shape of right pyramid on a square base on side 8cm and height 15cm a frastrum whose volume is a third of the pyramid is cut off determine height of frastrum
Let the height of the frustum be h cm.
Given:
Base side of the pyramid = 8 cm
Height of the pyramid = 15 cm
Volume of the pyramid = 1/3 * base area * height
Volume of the frustum = 1/3 * base area * height
Since the volume of the frustum is one-third of the pyramid:
Volume of frustum = 1/3 * 1/3 * volume of pyramid = 1/9 * volume of pyramid
Let's calculate the volume of the pyramid first.
Base area of the pyramid = side^2 = 8^2 = 64 cm^2
Volume of the pyramid = 1/3 * 64 * 15 = 320 cm^3
Now, calculate the volume of the frustum:
Volume of the frustum = 1/9 * 320 = 320/9 = 35.56 cm^3
Volume of frustum = 1/3 * (base area of the frustum + square root of base area of frustum times base area of the top) * h = 1/3 * 64 * h
35.56 = 64h/3
h = 35.56 * 3 / 64 = 1.67 cm
Therefore, the height of the frustum is 1.67 cm.