The volume of a sphere is 2,098pi m3. What is the surface area of the sphere to the nearest tenth?
1,700 m2
146.2 m2
850 m2
26,364 m2
It feels odd looking at these old posts, wondering where the original poster is now. Maybe in college, maybe even beyond that stage..
and they might never come back on here
it is so weird
4/3 pi r^3 = 2098 pi
r^3 = 15735
r^2 = 135.28
A = 4pi r^2 = 1700
they may not even know how much they've helped us and future students...
Yeah.. It really is weird. I was still a kid when all these questions were posted, meanwhile the people who posted them probably didn't get their answer(s) until too late. But thank goodness they are still here to help us, right?
I'm grateful nonetheless. Hope all of you are doing alright.
hope u guys r all doing great too
To find the surface area of a sphere, you'll need to know the volume of the sphere. However, in this case, you are given the volume of the sphere, which is 2,098π m³. To find the surface area, you need to reverse the formula for volume of a sphere.
The formula for the volume of a sphere is:
V = (4/3)πr³
Solving for r:
r³ = (3V) / (4π)
r = ∛[(3V) / (4π)]
Now, you can substitute the given volume into the equation and solve for r:
r = ∛[(3 * 2,098π) / (4π)]
r ≈ ∛(1,747.5)
r ≈ 12.88
Once you have the radius, you can calculate the surface area using the formula for the surface area of a sphere:
A = 4πr²
Substituting the value of r into the equation:
A ≈ 4π(12.88)²
A ≈ 4π(166.144)
A ≈ 664.576π
To find the approximated surface area to the nearest tenth, you can evaluate the numerical value of π and round the result appropriately. The closest approximation from the given options is:
A ≈ 664.576 * 3.14
A ≈ 2,086.4136
Rounding this value to the nearest tenth, the surface area of the sphere is approximately 2,086.4 m².