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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

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 t class=

Respuesta :

CastleRook
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
calculista

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

[tex]A=\pi r^{2}[/tex]

Step [tex]1[/tex]

Find the radius of the circular base

we know that

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

[tex]tan\ 70=\frac{r}{12}[/tex]

Solve for r

[tex]r=12*tan\ 70[/tex]

Step [tex]2[/tex]

Find the area of the base

substitute the value of the radius in the formula of area

[tex]A=\pi r^{2}[/tex]

[tex]A=\pi*(12*tan\ 70)^{2}\ ft^{2}[/tex]

therefore

the answer is the option a

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

[tex]A=\pi*(12*tan\ 70)^{2}\ ft^{2}[/tex]


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