Question

Bill needs to find the area of the ground covered by a conical tent. The tent is 12 feet tall and makes a 70° angle with the ground. Which expression can be used to find the area?

a) π · (12 · tan 70°)2


b) 36 · π


c) π · (12tan 70°12tan 70°)2


d) π · (tan 70°12tan 70°12)2

Answer 1

we know that

the area of the ground covered by the tent is a circular area

then

the area of a circle is equal to

`A=\pi r^(2)`

Step
`1`

Find the radius of the circular base

we know that

in the right triangle ABC-----> see the attached figure to better understand the problem

`tan\ 70=(r)/(12)`

Solve for r

`r=12*tan\ 70`

Step
`2`

Find the area of the base

substitute the value of the radius in the formula of area

`A=\pi r^(2)`

`A=\pi*(12*tan\ 70)^(2)\ ft^(2)`

therefore

the answer is the option a

the area of the ground covered by a conical tent is equal to

`A=\pi*(12*tan\ 70)^(2)\ ft^(2)`