Questions on Geometry: Bodies in space, right solid, cylinder, sphere answered by real tutors!

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Question 143957: A new hotel design includes a glass-enclosed cylindrical elevator. A scale model of the elevator is 1 foot high. The actual elevator will be 100 feet tall and 10 feet in diameter. What is the approximate area of a base of the model elevator? Round your answer to the nearest tenth inch.: A new hotel design includes a glass-enclosed cylindrical elevator. A scale model of the elevator is 1 foot high. The actual elevator will be 100 feet tall and 10 feet in diameter. What is the approximate area of a base of the model elevator? Round your answer to the nearest tenth inch.
Answer by vleith(1156) About Me  (Show Source):
You can put this solution on YOUR website!
Use ratios to find the diameter of the model.
1/100 = x/10
0.1 = x
The model diameter is .1
Area of a circle is A = pi*r^2
d = 2r
r = d/2
A = pi*(d/2)^2
A = pi* (.05)^2
A = 0.007853975 ft^2} <BR> i square foot = 144 square inches<BR> <IMG SRC=/cgi-bin/plot-formula.mpl?expression=Use+ratios+to+find+the+diameter+of+the+model.%0D%0A%0D%0A%3CIMG+SRC=%2Fcgi-bin%2Fplot-formula.mpl%3Fexpression=1%252F100%2B=%2Bx%252F10%26x=0003+ALIGN=MIDDLE+ALT=%221%2F100+=+x%2F10%22+BORDER=0+%3E%0D%0A%3CIMG+SRC=%2Fcgi-bin%2Fplot-formula.mpl%3Fexpression=0.1%2B=%2Bx%26x=0003+ALIGN=MIDDLE+ALT=%220.1+=+x%22+BORDER=0+%3E%0D%0A%0D%0AThe+model+diameter+is+.1%0D%0A%0D%0AArea+of+a+circle+is+%3CIMG+SRC=%2Fcgi-bin%2Fplot-formula.mpl%3Fexpression=A%2B=%2Bpi%252Ar%255E2%26x=0003+ALIGN=MIDDLE+ALT=%22A+=+pi%2Ar%5E2%22+BORDER=0+%3E%0D%0A%3CIMG+SRC=%2Fcgi-bin%2Fplot-formula.mpl%3Fexpression=d%2B=%2B2r%26x=0003+ALIGN=MIDDLE+ALT=%22d+=+2r%22+BORDER=0+%3E%0D%0A%3CIMG+SRC=%2Fcgi-bin%2Fplot-formula.mpl%3Fexpression=r%2B=%2Bd%252F2%26x=0003+ALIGN=MIDDLE+ALT=%22r+=+d%2F2%22+BORDER=0+%3E%0D%0A%0D%0A%3CIMG+SRC=%2Fcgi-bin%2Fplot-formula.mpl%3Fexpression=A%2B=%2Bpi%252A%2528d%252F2%2529%255E2%2B%26x=0003+ALIGN=MIDDLE+ALT=%22A+=+pi%2A%28d%2F2%29%5E2+%22+BORDER=0+%3E%0D%0A%3CIMG+SRC=%2Fcgi-bin%2Fplot-formula.mpl%3Fexpression=A%2B=%2Bpi%252A%2B%2528.05%2529%255E2%26x=0003+ALIGN=MIDDLE+ALT=%22A+=+pi%2A+%28.05%29%5E2%22+BORDER=0+%3E%0D%0A%3CIMG+SRC=%2Fcgi-bin%2Fplot-formula.mpl%3Fexpression=A%2B=%2B0.007853975%2Bft%255E2%257D%250D%250A%250D%250Ai%2Bsquare%2Bfoot%2B=%2B144%2Bsquare%2Binches%250D%250A%257B%257B%257BA%2B=%2B1.1309%2Bsquare%2Binches%26x=0003+ALIGN=MIDDLE+ALT=%22A+=+0.007853975+ft%5E2%7D%0D%0A%0D%0Ai+square+foot+=+144+square+inches%0D%0A&x=0003 ALIGN=MIDDLE ALT= 1/100 = x/10
0.1 = x
The model diameter is .1
Area of a circle is A = pi*r^2
d = 2r
r = d/2
A = pi*(d/2)^2
A = pi* (.05)^2