An inverted square pyramid has a height equal to 8m and a top edge to 3m. Initially, it contains water to the depth of 5m.
a. What is the initial volume of the water in the tank?
b. If the additional water is to be pumped into the tank at the rate of 20 gallons per minute, how many hours will it take to fill the tank?
vovo
JOhn kenneth gangoso
To find the initial volume of water in the tank, we need to calculate the volume of the inverted square pyramid.
a. The volume of an inverted square pyramid can be calculated using the formula:
Volume = (1/3) * base area * height
In this case, the base area is the square of the length of the top edge, and the height is 5m.
Step 1: Calculate the base area
Since the top edge of the inverted square pyramid is 3m, the base area is calculated by squaring the top edge.
Base area = (3m)^2 = 9m^2
Step 2: Calculate the volume
Using the formula, we can calculate the volume:
Volume = (1/3) * 9m^2 * 5m = 15m^3
So, the initial volume of water in the tank is 15 cubic meters.
b. To calculate how many hours it will take to fill the tank at a rate of 20 gallons per minute, we need to convert the volume from cubic meters to gallons and then find the time taken.
Step 1: Convert cubic meters to gallons
1 cubic meter is equal to 264.172 gallons.
15 cubic meters * 264.172 gallons/cubic meter = 3962.58 gallons
Step 2: Calculate the time
The rate at which the additional water is pumped is 20 gallons per minute.
To find the time taken, divide the total volume by the rate:
Time = 3962.58 gallons / 20 gallons per minute = 198.13 minutes
To convert minutes to hours, divide by 60:
Time = 198.13 minutes / 60 minutes per hour = 3.30 hours
Therefore, it will take approximately 3.30 hours to fill the tank.