Area Problem

**ur5pointos2slo** · October 3rd 2008, 03:54 PM

I have been stuck on this problem. Any help to get me started would be appreciated thanks.

A student in a stationary hot-air balloon is momentarily fixed at 1,325-ft elevation above a level piece of land. The pilot looks down( 60 degrees from the horizontal) and turns laterally 360 degrees.

a) how many acres are contained within the core generated by his line of sight?

b) how high would the balloon be if, when performing the same procedure an area 4 times greater is encompassed? (hint: 1 acre= 43,559.5 ft sq.)

**skeeter** · October 3rd 2008, 04:00 PM

you made a sketch, right?

$\tan(60) = \frac{1325}{r}$

where r is the radius of land on the surface within the "cone".

solve for r, then find the area of the circular plot of land in square feet ... you'll have to convert that to acres.

for an area 4 times greater, r would have to be doubled, right? why?

**ur5pointos2slo** · October 3rd 2008, 04:16 PM

Originally Posted by skeeter

you made a sketch, right?

$\tan(60) = \frac{1325}{r}$

where r is the radius of land on the surface within the "cone".

solve for r, then find the area of the circular plot of land in square feet ... you'll have to convert that to acres.

for an area 4 times greater, r would have to be doubled, right? why?

Yes I made a sketch and got r=764.98..so then I would need to use the surface area of a cone formula? I get 3676972.5 when I used the formula for that. So if I am converting correctly I get 84.4 acres. Is this correct?

r doubled? why wouldnt it have to be multiplied by 4?

thanks for quick reply too

**skeeter** · October 3rd 2008, 04:30 PM

not the surface area for a cone ... you're only trying to find the area of the land which is enclosed by a circle.

how much larger is $\pi(2r)^2$ than $\pi r^2$ ?

**ur5pointos2slo** · October 3rd 2008, 04:36 PM

Originally Posted by skeeter

not the surface area for a cone ... you're only trying to find the area of the land which is enclosed by a circle.

how much larger is $\pi(2r)^2$ than $\pi r^2$ ?

ok so i just need to use A= $\pi r^2$ to find the area that he is looking at?

and $\pi(2r)^2$ is twice the radius

**skeeter** · October 3rd 2008, 04:44 PM

Originally Posted by ur5pointos2slo

ok so i just need to use A= $\pi r^2$ to find the area that he is looking at?
and $\pi(2r)^2$ is twice the radius

yes, just $\pi r^2$

twice the radius results in four times the area.

**ur5pointos2slo** · October 3rd 2008, 04:45 PM

Originally Posted by skeeter

yes, just $\pi r^2$

twice the radius results in four times the area.

You are good. Thanks

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