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

1. anonymous

I got 4,464.88 in^2.

2. anonymous

Is it correct?

3. anonymous

@dan815 @pooja195 @ganeshie8

4. anonymous

@Hero

5. anonymous

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

6. anonymous

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

7. anonymous

Thanks!!

8. anonymous

@jdoe0001

9. anonymous

What we did earlier was wrong

10. 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.

11. anonymous

That's my work for my revision

12. Loser66

First off, you need find r Yes

13. Loser66

correct

14. anonymous

@Loser66

15. anonymous

what is correct?? XD

16. Loser66

The last one.

17. anonymous

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

18. Loser66

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

19. anonymous

Ok, thanks!

20. anonymous

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

21. Loser66

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

22. anonymous

But in the question it says it's the circumference

23. anonymous

hehe

24. anonymous

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

25. anonymous

lemme be back in a bit

26. anonymous

ok

27. anonymous

u got it??

28. anonymous

@jdoe0001

29. anonymous

@sewandowski ... hold the mayo

30. anonymous

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

31. anonymous

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

32. 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!

33. anonymous

k

34. mathstudent55

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

35. 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.

36. 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.