9514 1404 393
Answer:
1816.7 in³ ≈ 29,769.6 cm³
Step-by-step explanation:
The surface area of a sphere is given by the formula ...
A = 4πr²
Then the radius is ...
r = √(A/4π) = (1/2)√(A/π)
The volume of a sphere is given by the formula ...
V = 4/3πr³
Using the above value of r, we find the volume to be ...
V = (4/3)π(1/2)³(A/π)^(3/2) = 1/6√(A³/π) ≈ 1816.7 in³
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The answer is requested in cm³. The conversion factor is (2.54 cm/(1 in))³, so this volume is ...
(1816.7 in³)·(2.54 cm/(1 in))³ = 29,769.6 cm³
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<em>Additional comment</em>
We suspect an error in the problem statement, as the given units are square inches and the requested volume is in cubic centimeters. Usually, there would be an explicit statement regarding the necessity for units conversion.
The factored form would be (2x + 1)(x^2 - 7)
We can solve this by setting up a system of equations. We will use x for the $3 boxes and y for the $5 boxes:
x+y=34
3x+5y=130
We can use the elimination method by multiplying the first equation by 3:
3x+3y=102
3x+5y=130
0x-2y=-28
y=14
We can then plug this number back into one of the original equations to solve for x:
x+14=34
x=20
We can check these answers by plugging them into the equations:
20+14=34
34=34
(3)(20)+(5)(14)=130
60+70=130
130=130
Therefore, there are 20 of the $3 boxes, since we originally said that x would be the $3 boxes.
