A cone with a diameter of 7.2 meters and slant height of 8.8 meters is being filled with water at a rate of 2.5 m^3 per minute. How many minutes will it take to fill the cone?
We need the perpendicular height, not the slant height
h^2 + 3.6^2 = 8.8^2
h^2 = 64.48
h= √64.48
Volume = π(3.6)^2 (√64.48)
time to fill = π(12.96)√64.48 /2.5 = appr 130.78 minutes
Chapter one Quiz 3
to the heart tenth.
cone
S. Find the surface i
12 Chapter 12 Quiz 4
To find the number of minutes it will take to fill the cone, we need to determine the volume of the cone and divide it by the rate at which water is being filled.
First, let's calculate the radius of the cone. We know that the diameter is 7.2 meters, so the radius is half of that:
radius = diameter / 2 = 7.2 / 2 = 3.6 meters
Next, we can calculate the volume of the cone using the formula for the volume of a cone:
volume = (1/3) * π * r^2 * h
Where:
- π is a mathematical constant approximately equal to 3.14159
- r is the radius of the cone
- h is the height of the cone, which is equal to the slant height (8.8 meters) minus the radius
volume = (1/3) * π * (3.6)^2 * (8.8 - 3.6)
Calculating this expression, we find:
volume ≈ (1/3) * 3.14159 * (3.6)^2 * 5.2
volume ≈ 90.718 m^3
Now, we can divide the volume by the rate at which water is being filled to find the number of minutes it will take to fill the cone:
time = volume / rate
where the rate of filling is given as 2.5 m^3 per minute:
time = 90.718 m^3 / 2.5 m^3 per minute
time ≈ 36.29 minutes
Therefore, it will take approximately 36.29 minutes to fill the cone.