All High School Math Resources
Example Questions
Example Question #1 : Cones
What is the volume of a cone with a height of and a base with a radius of ?
To find the volume of a cone we must use the equation . In this formula, is the area of the circular base of the cone, and is the height of the cone.
We must first solve for the area of the base using .
The equation for the area of a circle is . Using this, we can adjust our formula and plug in the value of our radius.
Now we can plug in our given height, .
Multiply everything out to solve for the volume.
The volume of the cone is .
Example Question #1 : Solid Geometry
What is the equation of a circle with a center of (5,15) and a radius of 7?
To find the equation of a circle we must first know the standard form of the equation of a circle which is
The letters and represent the -value and -value of the center of the circle respectively.
In this case is 5 and k is 15 so plugging the values into the equation yields
We then plug the radius into the equation to get
Square it to yield
The equation with a center of (5,15) and a radius of 7 is .
Example Question #2 : Cones
Example Question #1 : Cones
What is the volume of a cone that has a radius of 3 and a height of 4?
The standard equation for the volume of a cone is
where denotes the radius and denotes the height.
Plug in the given values for and to find the answer:
Example Question #3 : Solid Geometry
Find the volume of the following cone.
The formula for the volume of a cone is:
where is the radius of the cone and is the height of the cone.
In order to find the height of the cone, use the Pythagorean Theorem:
Plugging in our values, we get:
Example Question #4 : Solid Geometry
Find the volume of the following cone.
The formula for the volume of a cone is:
Where is the radius of the cone and is the height of the cone
Use the Pythagorean Theorem to find the length of the radius:
Plugging in our values, we get:
Example Question #1 : Cones
Find the volume of the following half cone.
The formula of the volume of a half cone is:
Where is the radius of the cone and is the height of the cone.
Use the Pythagorean Theorem to find the height of the cone:
Example Question #1 : Cones
What is the volume of a right cone with a diameter of 6 cm and a height of 5 cm?
The general formula is given by , where = radius and = height.
The diameter is 6 cm, so the radius is 3 cm.
Example Question #1 : Cones
There is a large cone with a radius of 4 meters and height of 18 meters. You can fill the cone with water at a rate of 3 cubic meters every 25 seconds. How long will it take you to fill the cone?
First we will calculate the volume of the cone
Next we will determine the time it will take to fill that volume
We will then convert that into minutes
Example Question #2 : Cones
You have an empty cylinder with a base diameter of 6 and a height of 10 and you have a cone full of water with a base radius of 3 and a height of 10. If you empty the cone of water into the cylinder, how much volume is left empty in the cylinder?
Cylinder Volume =
Cone Volume =
Cylinder Diameter = 6, therefore Cylinder Radius = 3
Cone Radius = 3
Empty Volume = Cylinder Volume – Cone Volume