Make all the denominators equal
3/8 = 45/120
2/3 = 80/120
4/5 = 96/120
From least to greatest we have,
3/8, 2/3, 4/5
So we know that surface area is top circle +bottom circle+ (circumfurence times height so) 2(π(radius)^2)+(height(2π(r))) so fill in the blanks
it's kind of hard to see but πr means pi times radius (r)
2πr^2+((4.2)(2)(π)(r))=628.3
factor out the 2 so the equation would mean
2((πr^2)+(4.2πr))=628.3
divide both sides by 2
πr^2+4.2πr=314.15
what's interesting is that the first few digits of pi are 3.1415 so we aproximate pi as 3.14 and divide both sides by 3.1415
r^2+4.2r=100
subtract 100 from both sides
r^2+4.2r-100=0
factor
(x-8.11812)(x+12.3181)=0
so (if xy=0 then x or/and y must be 0 so)we set them to 0 so
x-8.11812=0
x=8.11812
second one
x+12.3181=0
x=-12.3181
since radii (or any legnth) cannot be negative, we can cross this solution out so
radius=8.11812
If you would like to know what is the area of the wall, you can calculate this using the following steps:
area = length * width
area = 9 1/3 feet * 8 1/8 feet = 28/3 feet * 65/8 feet = 455/6 = 75 5/6 square feet
The area of the wall is 75 5/6 square feet.
If the mural is 100 square feet, it won't fit on the wall, because 100 > 75 5/6.
