Challenge: The distance around the middle of a sphere (the circumference) equals 37.699 in. What is the surface area of the sphere?

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Challenge: The distance around the middle of a sphere (the circumference) equals 37.699 in. What is the surface area of the sphere?

Mathematics
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I got 4,464.88 in^2.
Is it correct?

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yeap \(\bf \textit{surface of a sphere}=4\pi r^2\qquad r=\cfrac{37.699}{2}\qquad 4\cdot \pi \cdot \left( \cfrac{37.699}{2} \right)^2 \approx 4464.88\)
\(\bf \textit{surface of a sphere}=4\pi r^2\qquad r=\cfrac{37.699}{2}\qquad \\ \quad \\ 4\cdot \pi \cdot \left( \cfrac{37.699}{2} \right)^2 \approx 4464.88\)
Thanks!!
What we did earlier was wrong
C = 2πr 37.699 = 2πr 37.699 / 2π = r 59.22 ≈ r The radius is approximately 59.22 inches. SA = 4π59.22^2 SA ≈ 44070.37 The surface area is approximately 44,070.37 in^2.
That's my work for my revision
First off, you need find r Yes
correct
what is correct?? XD
The last one.
heey, @jdoe0001 , what we did earlier was wrong, we thought the circumference was the diameter and worked from there
while I tried to guide you, you posted the correct one, so that I just say yes.
Ok, thanks!
hmmm the distance around the middle of a sphere, sounds to me like the diameter :)
@jdoe0001 Hey, invisible friend, no more invisible??? hahaha
But in the question it says it's the circumference
hehe
It's the distance AROUND, not the distance from one end to another
lemme be back in a bit
ok
u got it??
@sewandowski ... hold the mayo
so the circumference is 37.699 we also know that the circumference of any circle is \(2\pi r\) thus we could say that \(\bf circumference = 37.699\qquad circumference=2\pi r\qquad thus \\ \quad \\ 37.699=2\pi r\implies {\color{brown}{ \cfrac{37.699}{2\pi } }}=r \\ \quad \\ \quad \\ \textit{surface area}=4\pi {\color{brown}{ r}}^2\to 4\pi \cdot \left( {\color{brown}{ \cfrac{37.699}{2\pi } }} \right)^2\to 4\pi \cfrac{37.699^2}{2^2\pi^2}\to \cancel{4\pi} \cfrac{37.699^2}{\cancel{4\pi}\pi }\)
Heey, just finished the test, it was another answer :/
Nevermind, thanks for the help but I need help in another problem, so I'll close this one and make another one. Thanks anyways!
k
\(r = \dfrac{37.699 ~in.}{2 \pi} = 5.99998 ~in.\) \(A = 4 \pi r^2 = 4 \times \pi \times (5.99998~in.)^2 = 452.39~in.^2\)
@sewandowski Before you go look at this. You wrote above: C = 2πr 37.699 = 2πr 37.699 / 2π = r 59.22 ≈ r When you solve a problem, you need to do the operations, but you also need to confirm that answers make sense. If the circumference of a circle is approx. 38 in., how can the radius of the circle be 59.22 in.? It's impossible for the radius of a circle to be larger than the circumference.
Your mistake above is this: How do you calculate \(\dfrac{37.699}{2 \pi} \) ? You can use your calculator and calculat4e first 2 * pi = 6.28 Then do 37.699/6.28 Or you can do 37.699 / 2 / pi You need to divide 37.699 by 2 and divide the result by pi, not multiply by pi like you did.

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