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

- anonymous

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- katieb

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- anonymous

I got 4,464.88 in^2.

- anonymous

Is it correct?

- anonymous

@dan815 @pooja195 @ganeshie8

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## More answers

- anonymous

@Hero

- jdoe0001

yeap \(\bf \textit{surface of a sphere}=4\pi r^2\qquad r=\cfrac{37.699}{2}\qquad 4\cdot \pi \cdot \left( \cfrac{37.699}{2} \right)^2 \approx 4464.88\)

- jdoe0001

\(\bf \textit{surface of a sphere}=4\pi r^2\qquad r=\cfrac{37.699}{2}\qquad
\\ \quad \\
4\cdot \pi \cdot \left( \cfrac{37.699}{2} \right)^2 \approx 4464.88\)

- anonymous

Thanks!!

- anonymous

@jdoe0001

- anonymous

What we did earlier was wrong

- anonymous

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.

- anonymous

That's my work for my revision

- Loser66

First off, you need find r
Yes

- Loser66

correct

- anonymous

@Loser66

- anonymous

what is correct?? XD

- Loser66

The last one.

- anonymous

heey, @jdoe0001 , what we did earlier was wrong, we thought the circumference was the diameter and worked from there

- Loser66

while I tried to guide you, you posted the correct one, so that I just say yes.

- anonymous

Ok, thanks!

- jdoe0001

hmmm the distance around the middle of a sphere, sounds to me like the diameter :)

- Loser66

@jdoe0001 Hey, invisible friend, no more invisible??? hahaha

- anonymous

But in the question it says it's the circumference

- jdoe0001

hehe

- anonymous

It's the distance AROUND, not the distance from one end to another

- jdoe0001

lemme be back in a bit

- anonymous

ok

- anonymous

u got it??

- anonymous

@jdoe0001

- jdoe0001

@sewandowski ... hold the mayo

- jdoe0001

so the circumference is 37.699
we also know that the circumference of any circle is \(2\pi r\)
thus we could say that \(\bf circumference = 37.699\qquad circumference=2\pi r\qquad thus
\\ \quad \\
37.699=2\pi r\implies {\color{brown}{ \cfrac{37.699}{2\pi } }}=r
\\ \quad \\ \quad \\
\textit{surface area}=4\pi {\color{brown}{ r}}^2\to 4\pi \cdot \left( {\color{brown}{ \cfrac{37.699}{2\pi } }} \right)^2\to 4\pi \cfrac{37.699^2}{2^2\pi^2}\to \cancel{4\pi} \cfrac{37.699^2}{\cancel{4\pi}\pi }\)

- anonymous

Heey, just finished the test, it was another answer :/

- anonymous

Nevermind, thanks for the help but I need help in another problem, so I'll close this one and make another one. Thanks anyways!

- jdoe0001

k

- mathstudent55

\(r = \dfrac{37.699 ~in.}{2 \pi} = 5.99998 ~in.\)
\(A = 4 \pi r^2 = 4 \times \pi \times (5.99998~in.)^2 = 452.39~in.^2\)

- mathstudent55

@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.

- mathstudent55

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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