Answer to Question #146911 in Geometry for doggo

Question

An inverted regular square pyramid has an altitude of 12m and with top edge of 3m is fully–filled with water What is the volume of the water in m3? A portion of water is to be removed so that water will be 7m deep.

Answer 1

V = (1/3)*A*h

A = area of Base = b² = 3² = 9m²

h = altitude = 12m

V = (1/3)*9*12

V = 36m³

The volume of water when it's fully filled in the cylinder is 36m³.

If a portion of water is to be removed so that water will be 7m deep:

Final height, h = 7m

Initial height, H = 12m

Final base edge, b = bm

Initial base edge, B = 3m

(H/h) = (B/b)

(12/7) = (3/b)

Solving b = 1.75m

A = b² = 1.75² = 3.0625m²

V =(1/3)*A*h

V =(1/3)*3.0625*7

V = 7.146m³

The volume of the water in the cylinder when a portion is removed so that the water is 7m deep is 7.146m³.