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Example Questions
Example Question #1 : How To Find The Volume Of A Sphere
What is the volume of a sphere with a radius of ?
To solve for the volume of a sphere, you must first know the equation for the volume of a sphere.
In this equation, is equal to the radius. We can plug the given radius from the question into the equation for .
Now we simply solve for .
The volume of the sphere is .
Example Question #1 : How To Find The Volume Of A Sphere
What is the volume of a sphere with a radius of 4? (Round to the nearest tenth)
To solve for the volume of a sphere you must first know the equation for the volume of a sphere.
The equation is
Then plug the radius into the equation for yielding
Then cube the radius to get
Multiply the answer by and to yield .
The answer is .
Example Question #1 : How To Find The Volume Of A Sphere
For a sphere the volume is given by V = (4/3)πr3 and the surface area is given by A = 4πr2. If the sphere has a surface area of 256π, what is the volume?
750π
615π
683π
300π
683π
Given the surface area, we can solve for the radius and then solve for the volume.
4πr2 = 256π
4r2 = 256
r2 = 64
r = 8
Now solve the volume equation, substituting for r:
V = (4/3)π(8)3
V = (4/3)π*512
V = (2048/3)π
V = 683π
Example Question #2 : How To Find The Volume Of A Sphere
A typical baseball is in diameter. Find the baseball's volume in cubic centimeters.
Not enough information to solve
In order to find the volume of a sphere, use the formula
We were given the baseball's diameter, , which must be converted to its radius.
Now we can solve for volume.
Convert to centimeters.
If you arrived at then you did not convert the diameter to a radius.
Example Question #2 : How To Find The Volume Of A Sphere
What is the volume of a sphere whose radius is .
Not enough information to solve
In order to find the volume of a sphere, use the formula
We were given the radius of the sphere, .Therefore, we can solve for volume.
If you calculated the volume to be then you multiplied by rather than by .
Example Question #3 : How To Find The Volume Of A Sphere
To the nearest tenth of a cubic centimeter, give the volume of a sphere with surface area 1,000 square centimeters.
The surface area of a sphere in terms of its radius is
Substitute and solve for :
Substitute for in the formula for the volume of a sphere:
Example Question #4 : How To Find The Volume Of A Sphere
Find the volume of the following sphere.
The formula for the volume of a sphere is:
where is the radius of the sphere.
Plugging in our values, we get:
Example Question #2 : How To Find The Volume Of A Sphere
Find the volume of the following sphere.
The formula for the volume of a sphere is:
Where is the radius of the sphere
Plugging in our values, we get:
Example Question #2 : How To Find The Volume Of A Sphere
The specifications of an official NBA basketball are that it must be 29.5 inches in circumference and weigh 22 ounces. What is the approximate volume of the basketball? Remember that the volume of a sphere is calculated by V=(4πr3)/3
3468.05 cu.in.
138.43 cu.in.
434.19 cu.in.
8557.46 cu.in.
92.48 cu.in.
434.19 cu.in.
To find your answer, we would use the formula: C=2πr. We are given that C = 29.5. Thus we can plug in to get [29.5]=2πr and then multiply 2π to get 29.5=(6.28)r. Lastly, we divide both sides by 6.28 to get 4.70=r. Then we would plug into the formula for volume V=(4π〖(4.7)〗3) / 3 (The information given of 22 ounces is useless)
Example Question #4 : How To Find The Volume Of A Sphere
What is the volume of a sphere with a diameter of ?
The formula for volume of a sphere is .
The problem gives us the diameter, however, and not the radius. Since the diameter is twice the radius, or , we can find the radius.
.
Now plug that into our initial equation.
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