Question

The circle formed by the blades of a fan has a circumference of thirty-seven and five-sevenths inches. What is its diameter? Use twenty-two sevenths for pi.

twelve inches

eighteen inches

twenty-one inches

twenty-six inches

Answer 1

We would need the formula for Circumference of a circle in terms of its diameter. Do you have that equation?

Answer 2

no

Answer 3

\( C = 2 \pi r = \pi d \)
Does this equation seem familiar then?

Answer 4

no not really srry

Answer 5

It is fine. I recommend knowing this one, though, because it is important for these types of problems.

With that, we had some information from the word problem that we can substitute in to find d.
The circle formed by the blades of a fan has a[[ circumference of thirty-seven and five-sevenths inches]]. What is its diameter? Use [[twenty-two sevenths for pi.]]

Answer 6

What does "circumference is thirty-seven and five-sevenths" translate to with symbols? (Like, C = ..)

Answer 7

wat? sry didnt understand that

Answer 8

Our goal is to solve for d from this equation: \( C = \pi d \)
From this information, we can find a value for C: "circumference is thirty-seven and five-sevenths"
That value of C goes into the equation:
\( \_\_ = \pi d \)

Answer 9

oh ok then wat

Answer 10

then we use the approximation for \( \pi \): \( \pi \approx \dfrac{22}{7} \)
\( \_\_ = \dfrac{22}{7} d \)
where the blank is filled out with the value of circumference. We simply solve for d by removing its coefficient.

Answer 11

ok

Answer 12

then wat

Answer 13

you would be done. The value of d will be the diameter, the answer.

Answer 14

but wat is the the value of d?

Answer 15

Did you follow the steps above?
\( C = \pi d \)
\( C = \dfrac{22}{7} d \) <-- substitute C=__ here, then solve for d .
\( \_\_ = \dfrac{22}{7} d \)

Answer 16

i dont get it

Answer 17

which part does not make sense?

Answer 18

how am i gonig to solve for d?

Answer 19

i dont get the way u put it

Answer 20

let me back up, what is the value of our circumference given in the problem?
this is what goes in the blank.

Answer 21

ok

Answer 22

then

Answer 23

you haven't answered the question:
what is the value of our circumference given in the problem?

Answer 24

its 37, 5/7

Answer 25

yup.
so we put this in for the blank
37 5/7 = 22/7 d
now we have to divide both sides by the 22/7 that is multiplied to d.

Answer 26

37 5/7 / (22/7) = (22/7) / (22/7) d divided 22/7 from both sides
37 5/7 / (22/7) = d
that makes sense?

Answer 27

kinda

Answer 28

where do i divided 22/7?

Answer 29

i just see a bunch of numbers

Answer 30

let me go back and try to make this easier:
\( 37 \dfrac{5}{7} = \dfrac{22}{7} d \)
we should convert 37 5/7 to a mixed fraction. we'd multiply 37 by 7 and add it to the numerator like this:
\( \dfrac{37\times 7 + 5}{7} = \dfrac{22}{7} d \)

\( \dfrac{264}{7} = \dfrac{22}{7} d \) it might be easier, rather than do that full step, to just take it in smaller steps:
\( \dfrac{264}{\cancel{7}} \color{green}{\times \cancel{7}} = \dfrac{22}{\cancel{7}} d \color{green}{\times \cancel{7}} \)
\( 264 = 22 d \)

Answer 31

ok then wat?

Answer 32

the last step is dividing both sides by the 22, thus getting d alone. see how to do that?

Answer 33

\( \dfrac{264}{22} = \dfrac{\cancel{22}}{\cancel{22}} d \)
this is something for a calculator: 264/22, but you should find it comes out nicely

Answer 34

oh ok thx so much 4 ur help

Answer 35

the answer is 12in.

Answer 36

yup. glad to help. :)