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4. Mr. Bernard wants to put a small display table in the front of the restaurant featuring some of the shop’s new desserts and side dishes. The display table is a circular table with a diameter of 32 in. Mr. Bernard wants to put fabric over the table that hangs an additional 5 in. off the table. When he goes to the fabric store, Mr. Bernard finds that it sells fabric in rolls that have a width of 50 in., and the length is cut by the inch. Mr. Bernard purchases the minimum amount of fabric he needs. Then he cuts the fabric into a circular shape to cover the table with 5 in. of fabric hanging over the side. How many square inches of the fabric did Mr. Bernard have left over? Show all your work

Respuesta :

apologiabiology
ok assuming that when he buys the fabric, he cuts pieces off to make it fit, but doesn't sow them in other places to make up the lost area

so
first find the area of tablecloth he needs to buy
area=pir^2
diameter=32
d=2r
r=d/2
r=32/2=16
adds 5 inches extra
16+5=21
r=21
area of cloth=pi21^2
are of cloth=441pi
aprox pi=3.14
area=441 tmes 3.14
area=1384.74


buys cloth with width of 50 and legnth of x
so we need 2 things
1. area of cloth bought>area of tablecloth
2. legnth &width must both be greater or equal to the diameter of the tablecloth (so we can make a circle fit)

new diameter=32+5+5=42 (2 sides)
so
l and w must both be greater than or equal to 42
 
50l>1384.74
divide both sides by 50 to find legnth
l>27.6948
but the legnth must be also greater than or equal to 42
so make l=42 for min legnth
area of cloth bought=lw=42 by 50=42 times 50=2100

so we do

area wasted=area bought-area needed
area needed=area of tablecloth=1384.74
area bought=2100
area wasted=2100-1384.74
area wasted=715.26 in^2


answer is wasted area=715.26 square inches




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