SOLUTION: An inverted square pyramid has a height equal to 12 m and a top equal to 6 m. Initially, it contains a water depth of 9m. a. What is the initial volume of the water in the tank?

Algebra.Com
Question 1101394: An inverted square pyramid has a height equal to 12 m and a top equal to 6 m. Initially, it contains a water depth of 9m.
a. What is the initial volume of the water in the tank?

b. If additional water is to be pumped into the tank at the rate of 25 gallons per minute, how many hours will it take to fill the tank?

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


I assume the 6m is the length of a side of the square base....

The volume of the pyramid (in cubic meters) is one-third base times height:


When the tank is filled to 3/4 of its depth (9m, out of the total height of 12m), the volume of water is (3/4)^3 of the volume of the whole tank.

That statement uses the powerful general principle concerning similar figures: if the scale factor is a:b, then the ratio of areas is a^2:b^2, and the ratio of volumes is a^3:b^3.

So the volume of water in the tank when the depth is 9m is 27/64 of the total volume:

The volume still remaining in the tank is (1-(27/64)) = 37/64 of the total volume of the tank:

That's the interesting part of the problem.
I leave it to you to convert that volume in cubic meters to gallons, and to find the amount of time it takes to finish filling the tank at 25 gallons per minute.

RELATED QUESTIONS

.An inverted square pyramid has a height equal to 8m and a top edge equal to 3m.... (answered by ikleyn)
.An inverted square pyramid has a height equal to 8m and a top edge equal to 3m.... (answered by ikleyn)
An inverted square pyramid has a height equal to 8 meters and a top edge to 3 meters.... (answered by KMST)
Good day, can you help me with this problem? An inverted square pyramid has a height (answered by KMST)
An inverted regular pyramid whose square base has an area of 16 square units and a height (answered by KMST)
A regular triangular pyramid with a slant height of 9 m has a volume equal to 50 cu. m.... (answered by greenestamps)
A regular triangular pyramid with a slant height of 9m has a volume equal to 50 cubic... (answered by greenestamps)
Tank A and Tank B are rectangular prisms and are sitting on a flat table. Tank A is 10... (answered by CPhill)
A rectangular tank measures 4 m long, 2 m wide and 4.8 m high. Initially it is half... (answered by Cromlix)