Question

A stained-glass window is being designed in the shape of a rectangle surmounted by a semicircle, as shown in the figure. The width of the window is to be 3 feet, but the height h is yet to be determined. If 21 ft2 of glass is to be used, find the height h. (Round your answer to two decimal places.)

Answer 1

@escolas

Answer 2

I got the answer of 5.82... But webassign isn't taking that as an answer.. so I'm confused

Answer 3

Interesting..do you know if it means a half circle when it says semi-circle? I guess maybe it'd have to be, right?

Answer 4

Yeah, to find the area of the semi circle the formula is A=1/2piR^2

Answer 5

I made R capital because i didn't want anyone to get confused with pir lol

Answer 6

Which would mean the window has a height of the rectangle + the radius of the circle. Haha, yes that's right.

Answer 7

Yup

Answer 8

So I attempted to do that. I found the area of the half circle and then subtracted that from 21. Divided the 17.something by 3 to get the height and got 5.82.

Answer 9

So the semicircle is \[\frac{1}{2}\pi r^2 \rightarrow \frac{1}{2} \pi(3)^2=4.5\pi\]

Answer 10

Did you get that?

Answer 11

the diameter of the semicircle is 3, they want the radius. so it would be 1.5 not 3

Answer 12

At least I think?

Answer 13

You are 100% right.

Answer 14

Okay, just making sure I didn't make any little mistakes, I tend to do that a lot

Answer 15

Haha so did you take that number and subtract it from 21?

Answer 16

yeah
Then divided by three

Answer 17

wait, after I divide it by three shouldn't I add three?

Answer 18

well, i tried, and still wrong. lol

Answer 19

no, it would be 1.5

Answer 20

jeesh hahaha

Answer 21

Yes, axactly. Add 1.5 to the 5.82 or whatever. Does that work?

Answer 22

I forgot that last step, its correct with an answer of 7.32!

Answer 23

Haha awesome! You did that all on your own really!

Answer 24

I'm capable of math, I just need someone there to remind me of little things sometimes. I like the way you help because it reminds me of the way my boyfriend helps me. And with him I really start to understand and do it on my own. Lol

Answer 25

So a big thank you!