The circular bases of the traditional teepees of the Sioux and Cheyenne tribes have a diameter of about 15 ft. What is the area
of the base? Round to the nearest square unit.
A. 177 ft2
B. 47 ft2
C. 707 ft2
D. 24 ft2
2 answers:
if the diameter is 15, its radius is half that, or 7.5
![\bf \textit{area of a circle}\\\\A=\pi r^2~~\begin{cases}r=radius\\[-0.5em]\hrulefill\\r=7.5\end{cases}\implies A=\pi 7.5^2\implies A=56.25\pi \\\\\\A\approx 176.71459\implies A = \stackrel{\textit{rounded up}}{177}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20a%20circle%7D%5C%5C%5C%5CA%3D%5Cpi%20r%5E2~~%5Cbegin%7Bcases%7Dr%3Dradius%5C%5C%5B-0.5em%5D%5Chrulefill%5C%5Cr%3D7.5%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Cpi%207.5%5E2%5Cimplies%20A%3D56.25%5Cpi%20%5C%5C%5C%5C%5C%5CA%5Capprox%20176.71459%5Cimplies%20A%20%3D%20%5Cstackrel%7B%5Ctextit%7Brounded%20up%7D%7D%7B177%7D)
Answer:
A. 177 ft²
Step-by-step explanation:
To solve solve the area of the base, we learnt that the base is circular, so we will simply use the formula for finding area of circle to solve;
A = π r²
where r = radius
π is a constant
A= area of a circle
From the question given;
diameter is 15 ft, but radius is half of diameter, this implies that r = d/2 =15/2= 7.5 ft
π≈3.14
We can now proceed to insert our values into the formula;
A ≈ 3.14 × 7.5²
≈3.14×56.25
≈176.625
≈177 ft²
Therefore, the area of the base is 177 ft² approximately.
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