All GED Math Resources
Example Questions
Example Question #571 : Geometry And Graphs
You are 3D printing a ball which will be an integral piece to the project you are creating. If you need the ball to have a radius of 12cm, what volume of material will be required?
You are 3D printing a ball which will be an integral piece to the project you are creating. If you need the ball to have a radius of 12cm, what volume of material will be required?
We are asked to find the volume of a sphere, to do so, we should use the formula for volume of a sphere.
So, let's plug in our radius and solve:
So our answer is:
Example Question #571 : Geometry And Graphs
You are given a spherical floating speaker for your birthday. If the speaker has a radius of 5 inches, what is its volume?
You are given a spherical floating speaker for your birthday. If the speaker has a radius of 5 inches, what is its volume?
We need to find the volume of a sphere. To do so, we need the following formula:
We know r is 5, so just plug and simplify
Example Question #572 : Geometry And Graphs
A sphere has surface area . Give its volume.
The formula for the surface area of a sphere, given its radius , is
.
Set and solve for to get the radius.
Divide both sides by :
Take the positive square root of both sides to obtain the radius:
The formula for the volume of a sphere, given its radius , is
Substitute for in this formula and evaluate the expression:
Example Question #572 : Geometry And Graphs
A ball in the shape of a sphere has a radius of inches. What volume of air, in cubic inches, is needed to fully inflate the ball?
Recall how to find the volume of a sphere:
Plug in the given radius to solve for the volume.
Make sure to round to two places after the decimal point.
Example Question #574 : Geometry And Graphs
A sphere has a radius of . Find its volume.
The formula for the volume of a sphere is , with standing for radius. Since you know that the radius of the sphere is , all you have to do is plug in for and solve. Once you do that you learn that the volume is .
Example Question #573 : Geometry And Graphs
A spherical water balloon has a diameter of inches. How many water balloons of this size can be completely filled up with of water?
Start by finding the volume of one water balloon.
Recall how to find the volume of a sphere:
Plug in the given value for the radius.
Now, since one water balloon will require of water, divide the total volume of water by this value to find how many balloons can be filled.
Since the question asks for the number of complete balloons that can be filled, we will have to round down to the nearest whole number, .
Example Question #576 : Geometry And Graphs
Consider a tube which is 3 ft wide and 18 ft long.
Find the volume of the largest sphere which could fit within the tube described above.
Consider a tube which is 3 ft wide and 18 ft long.
Find the volume of the largest sphere which could fit within the tube described above.
To find the volume of a sphere, we simply need its radius
Now, the largest sphere which will fit within the tube will need to have a radius equal to the tube. Therefore, we can say our radius must be half the diameter, making it 1.5 ft.
Next, plug 1.5 ft into our formula to find our Volume
So, our answer is:
Example Question #1541 : Ged Math
If a sphere has a radius of and a circumference of , what is the volume?
This problem is deceptively simple. In order to solve for the volume of a sphere, all you need is the formula: , where r is the radius.
This problem has provided additional information alongside the pertinent information. We don't need to know what the circumference is if we have been provided with the radius.
Therefore, this problem can be quickly solved for by substituting for in the volume formula.
therefore, the volume of this sphere is
Example Question #1542 : Ged Math
What is the volume of a sphere if it has a diameter of ?
Not enough information
This problem is deceptively simple. In order to solve for the volume of a sphere, all you need is the formula: , where r is the radius.
This problem has provided us with the diameter, so we just need to do a little bit of work to solve for the radius. What is the relationship between radius and diameter? The diameter is twice the radius. Or in math speak: . This means we can solve for our radius by taking half of the diameter. Therefore, the radius will be
Now that we have r, we can substitute in the value for r and solve for the volume!
Example Question #1543 : Ged Math
If the volume of a sphere is , what is the radius?
This problem is very easy to solve as long as you have the volume formula for a sphere handy.
The formula is , where r is the radius.
The problem provides us with V, the volume. If we substitute in the volume, the only unknown in the problem is r. This is exactly what we want.
The goal is to get r by itself. We can begin this process by dividing by .
Now we may multiply both sides of the equation by to remove the fraction from the right side of the equals sign. This allows us to get closer to solving for r.
Now we need to take the cubed root of each side and we will have solved for the radius!