Question

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

Answer 1

I got 4,464.88 in^2.

Answer 2

Is it correct?

Answer 3

@dan815 @pooja195 @ganeshie8

Answer 4

@Hero

Answer 5

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

Answer 6

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

Answer 7

Thanks!!

Answer 8

@jdoe0001

Answer 9

What we did earlier was wrong

Answer 10

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.

Answer 11

That's my work for my revision

Answer 12

First off, you need find r
Yes

Answer 13

correct

Answer 14

@Loser66

Answer 15

what is correct?? XD

Answer 16

The last one.

Answer 17

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

Answer 18

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

Answer 19

Ok, thanks!

Answer 20

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

Answer 21

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

Answer 22

But in the question it says it's the circumference

Answer 23

hehe

Answer 24

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

Answer 25

lemme be back in a bit

Answer 26

ok

Answer 27

u got it??

Answer 28

@jdoe0001

Answer 29

@sewandowski ... hold the mayo

Answer 30

so the circumference is 37.699
we also know that the circumference of any circle is \(2\pi r\)

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

Answer 31

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

Answer 32

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

Answer 33

k

Answer 34

\(r = \dfrac{37.699 ~in.}{2 \pi} = 5.99998 ~in.\)

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

Answer 35

@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.

Answer 36

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.