Respuesta :
Answer:
B. 14
Step-by-step explanation:
We have been that an native American tepee is a conical tent. The tepee is 10 ft. in diameter and 12 ft. high.
First of all let us find the curved area of tepee by using curved area of cone formula.
[tex]\text{Curved area of cone}=\pi rl[/tex], where,
l = Slant height of cone,
r = Radius of cone.
Let us divide diameter of cone by 2 to get the radius of cone.
[tex]\text{Radius of cone}=\frac{10}{2}[/tex]
[tex]\text{Radius of cone}=5[/tex]
Now we will find the slant height of cone using Pythagoras theorem.
[tex]l^2=h^2+r^2[/tex]
[tex]l^2=12^2+5^2[/tex]
[tex]l=\sqrt{144+25}[/tex]
[tex]l=\sqrt{169}=13[/tex]
Upon substituting our given values in area formula we will get,
[tex]\text{Area of cone}=\pi*5*13[/tex]
[tex]\text{Area of cone}=3.14*65[/tex]
[tex]\text{Area of cone}=204.1[/tex]
Therefore, the area of cone is 204.1 square feet.
Now let us divide the area of cone by area covered by each skin to get the number of skin needed.
[tex]\text{Number of skins needed}=\frac{204.1\text{ ft}^2}{\text{15 ft}^2}[/tex]
[tex]\text{Number of skins needed}=13.6066666666666667\approx 14[/tex]
Therefore, 14 skins are needed to cover the tepee and option B is the correct choice.
