The volume that is inside the larger cylinder shown but outside the cylinder with the smaller radius, r, can be found with the formula below.
V = 250π – 10πr²
V is the volume inside the larger cylinder but outside the smaller cylinder in cubic centimeters.
r is the radius of the smaller cylinder in centimeters.
Which equation and solution gives the radius of the smaller cylinder if the volume inside the larger cylinder but outside the smaller cylinder is 160π centimeters³?
160π = 250π – 10πr²
r = 2
160π = 250π – 10πr²
r = 3
V = 250π – 10π(4)²
V = 90
To find the radius ( r ) of the smaller cylinder when the volume ( V ) inside the larger cylinder but outside the smaller cylinder is given as ( 160pi ) cm³, we start with the equation:
[
160pi = 250pi – 10pi r^2
]
First, we’ll simplify this equation. Let’s divide everything by ( pi ):
[
160 = 250 – 10r^2
]
Now, rearrange the equation to solve for ( r^2 ):
[
10r^2 = 250 – 160
]
[
10r^2 = 90
]
[
r^2 = 9
]
Now, take the square root of both sides:
[
r = 3
]
Thus, the correct equation and solution that gives the radius of the smaller cylinder is:
160π = 250π – 10πr², r = 3
This means the radius of the smaller cylinder is 3 cm. If you need further assistance or have additional questions, feel free to ask!
To find the radius of the smaller cylinder when the volume V is equal to 160π, we start with the equation:
[
160π = 250π – 10πr²
]
Now, let’s solve for r:
1. Subtract 250π from both sides:
[
160π – 250π = -10πr²
]
This simplifies to:
[
-90π = -10πr²
]
2. Divide both sides by -10π:
[
9 = r²
]
3. Take the square root of both sides:
[
r = 3
]
So, the correct answer is:
160π = 250π – 10πr²; r = 3.
This means that when the volume outside the smaller cylinder but inside the larger cylinder is 160π cm³, the radius of the smaller cylinder (r) is 3 cm. Great job on solving this! If you need further help, feel free to ask or check the extended services page for more assistance!
To find the radius ( r ) of the smaller cylinder when the volume ( V ) is 160π cm³, we start with the given equation:
[
160π = 250π – 10πr²
]
Now, let’s simplify the equation step by step:
1. Subtract 250π from both sides:
[
160π – 250π = -10πr²
]
This simplifies to:
[
-90π = -10πr²
]
2. Divide both sides by -10π (noting that π is positive and can be canceled out):
[
9 = r²
]
3. Take the square root of both sides:
[
r = 3
]
So, the correct solution is:
– ( r = 3 )
This means the radius of the smaller cylinder is 3 centimeters when the volume outside the smaller cylinder but inside the larger cylinder is 160π cm³.
To find the radius of the smaller cylinder when the volume ( V ) is ( 160pi ), we can start from the given equation:
[ 160pi = 250pi – 10pi r^2 ]
Now, let’s simplify and solve for ( r ).
1. Subtract ( 250pi ) from both sides:
[
160pi – 250pi = -10pi r^2
]
This simplifies to:
[
-90pi = -10pi r^2
]
2. Divide both sides by ( -10pi ):
[
9 = r^2
]
3. Take the square root of both sides:
[
r = 3
]
So the correct answer is:
160π = 250π – 10πr²
r = 3
This means the radius of the smaller cylinder is 3 cm. Well done for working through it! If you have more questions or need further assistance, feel free to ask!