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An oblique cone has a diameter of 12 units and a volume of 120π or 376.99 cubic units. What is the height of the cone?
units
Find the volume of the oblique pyramid with a square base. Note that the figure is not to scale. Round your answer to the nearest hundredth if necessary.
Enter your answer
To find the height of the oblique cone, we can use the formula for the volume of a cone:
[
V = frac{1}{3} pi r^2 h
]
where ( V ) is the volume, ( r ) is the radius, and ( h ) is the height.
Given that the diameter of the cone is 12 units, the radius ( r ) is:
[
r = frac{d}{2} = frac{12}{2} = 6 text{ units}
]
Now, we know the volume ( V = 120pi ). Plugging the values into the volume formula, we have:
[
120pi = frac{1}{3} pi (6^2) h
]
This simplifies to:
[
120pi = frac{1}{3} pi (36) h
]
Multiplying both sides by 3 to eliminate the fraction:
[
360pi = 36pi h
]
Next, we can divide both sides by ( 36pi ) to solve for ( h ):
[
h = frac{360pi}{36pi} = 10 text{ units}
]
So, the height of the cone is 10 units.
For the second part of your question regarding the volume of the oblique pyramid with a square base
To find the height of the oblique cone, we can use the formula for the volume of a cone:
[
V = frac{1}{3} pi r^2 h
]
where ( V ) is the volume, ( r ) is the radius, and ( h ) is the height.
1. First, we need to find the radius from the diameter. The diameter is given as 12 units, so the radius ( r ) is:
[
r = frac{diameter}{2} = frac{12}{2} = 6 , text{units}
]
2. Now, we can plug the values into the volume formula. We know that the volume ( V = 120pi ):
[
120pi = frac{1}{3} pi (6^2) h
]
3. Simplify the equation:
[
120pi = frac{1}{3} pi (36) h
]
[
120pi = 12pi h
]
4. To isolate ( h ), divide both sides by ( 12pi ):
[
h = frac{120pi}{12pi} = frac{120}{12} = 10 , text{units}
]
So, the height of the cone is 10 units.
Now for the oblique