1. ## Area Problem

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.)

2. 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?

3. Originally Posted by skeeter

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

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?

4. 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 $\pi r^2$ ?

5. 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

6. 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.

7. Originally Posted by skeeter
yes, just $\pi r^2$

twice the radius results in four times the area.
You are good. Thanks