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The dimensions are approximately 191 inches by 6.28 inches.
This produces a cylinder with about a 2 inch interior diameter, 1 inch radius, and a cross section of 3.14 square inches, 191 inches long.
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Area of the rectangle, A = LW =1200 in^2
where A is also the lateral area of the cylinder L.A.
L.A. = 2(pi)rh
Volume of the cylinder, V = (pi)(r^2)(h) = 600 in^3
Now, let's find the height and the radius of the cylinder.
Let denote W with x, and let W be the height, so h = x. So, L = 1200/x. Let L to be the circumference of the base, so C = L. So we need to find the radius.
C = 2(pi)r
1200/x = 2(pi)r
600/x = (pi)r
r = 600/[(pi)x]
Let's substitute what we know into the volume formula:
V = (pi)(r^2)(h)
600 = (pi)[600/((pi)x)]^2](x)
600 = (pi)[(3600/[(pi)^2)(x^2)](x)
600 = (pi)[3600/(pi)^2)(x^2)](x)
1 = 600/[x(pi)]
x(pi) = 600
x = 600/pi So,
W = x = 191 in (approximately). Then,
L = 1200/191
L = 6.28 in
Or you can work like this: Since,
L.A. = 2(pi)rh = 1200
h = 600/[(pi)r] Substitute h into the volume formula and find r;
V = (pi)(r^2)(h)
600 = (pi)(r^2)[600/((pi)r)]
1 = r substitute r into the height formula;
h = 600/[(pi)r]
h = 600/[(pi)(1)]
h = 600/(pi)
h = 191 So,
h = L = 191 in, and
W = 1200/h = 1200/191
W = 6.28 in
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