How to find the diameter of a sphere - ACT Math
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If a sphere has a volume of 
, what is its diameter?
If a sphere has a volume of
1. Use the volume to find the radius:
2. Use the radius to find the diameter:
1. Use the volume to find the radius:
2. Use the radius to find the diameter:
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A sphere has a volume of 
. What is its diameter?
A sphere has a volume of
This question relies on knowledge of the formula for volume of a sphere, which is as follows: 
In this equation, we have two variables, 
and 
. Additionally, we know that 
and 
is unknown. You can begin by rearranging the volume equation so it is solved for 
, then plug in 
and solve for 
:
Rearranged form:
Plug in 
for V
Simplify the part under the cubed root
-
Cancel the 
's since they are in the numerator and denominator.
-
Simplify the fraction and the 
:
Thus we are left with
Then, either use your calculator and enter 
Or recall that 
in order to find that 
.
We're almost there, but we need to go a step further. Dodge the trap answer "
" and carry on. Read the question carefully to see that we need the diameter, not the radius.
So
is our final answer.
This question relies on knowledge of the formula for volume of a sphere, which is as follows:
In this equation, we have two variables,
Rearranged form:
Plug in
Simplify the part under the cubed root
-
Cancel the
-
Simplify the fraction and the
Thus we are left with
Then, either use your calculator and enter
We're almost there, but we need to go a step further. Dodge the trap answer "
So
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A spherical plastic ball has a diameter of 
. What is the volume of the ball to the nearest cubic inch?
A spherical plastic ball has a diameter of
To answer this question, we must calculate the volume of the ball using the equation for the volume of a sphere. The equation for the volume of a sphere is four-thirds multiplied by pi, which is then multiplied by the radius cubed. The equation can be written like this:
We are given the diameter of the sphere in the problem, which is 
. To get the radius from the diameter, we divide the diameter by 
. So, for this data:
We can then plug our newly found radius of two into the equation to find the volume. For this data:
We then multiply 
by 
.
We finally substitute 3.14 for pi and multiply again to get our answer.
The question asked us to round to the nearest whole cubic inch. To do this, we round a number up one place if the last digit is a 5, 6, 7, 8, or 9, and we round it down if the last digit is a 1, 2, 3, or 4. Therefore:
Therefore our answer is 
.
To answer this question, we must calculate the volume of the ball using the equation for the volume of a sphere. The equation for the volume of a sphere is four-thirds multiplied by pi, which is then multiplied by the radius cubed. The equation can be written like this:
We are given the diameter of the sphere in the problem, which is
We can then plug our newly found radius of two into the equation to find the volume. For this data:
We then multiply
We finally substitute 3.14 for pi and multiply again to get our answer.
The question asked us to round to the nearest whole cubic inch. To do this, we round a number up one place if the last digit is a 5, 6, 7, 8, or 9, and we round it down if the last digit is a 1, 2, 3, or 4. Therefore:
Therefore our answer is
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A boulder breaks free on a slope and rolls downhill. It rolls for 
complete revolutions before grinding to a halt. If the boulder has a volume of 
cubic feet, how far in feet did the boulder roll? (Assume the boulder doesn't lose mass to friction). Round 
to 3 significant digits. Round your final answer to the nearest integer.
A boulder breaks free on a slope and rolls downhill. It rolls for
The formula for the volume of a sphere is:
To figure out how far the sphere rolled, we need to know the circumference, so we must first figure out radius. Solve the formula for volume in terms of radius:
Since the answer asks us to round to the nearest integer, we are safe to round 
to 
at this point.
To find circumference, we now apply our circumference formula:
If our boulder rolled 
times, it covered that many times its own circumference.
Thus, our boulder rolled for 
The formula for the volume of a sphere is:
To figure out how far the sphere rolled, we need to know the circumference, so we must first figure out radius. Solve the formula for volume in terms of radius:
Since the answer asks us to round to the nearest integer, we are safe to round
To find circumference, we now apply our circumference formula:
If our boulder rolled
Thus, our boulder rolled for
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Find the diameter of a sphere whose radius is 
.
Find the diameter of a sphere whose radius is
To solve, simply remember that diameter is twice the radius. Don't be fooled when the radius is an algebraic expression and incorporates the arbitrary constant 
. Thus,
To solve, simply remember that diameter is twice the radius. Don't be fooled when the radius is an algebraic expression and incorporates the arbitrary constant
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