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

$tan\ 70=\frac{r}{12}$

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

$A=\pi*(12*tan\ 70)^{2}\ ft^{2}$

Answer 2

To get the area of the cone we need to find the radius first.
tan 70=r/12
r=12tan 70
area of a circle is given by:
A=πr²
thus the area of the ground covered by the tent will be:
A=π(12tan70)²
The answer is 
A] A=π(12tan70°)²