W - a width
3w - a length
27 ft² - an area
Therefore:
w · 3w = 27
3w² = 27 |:3
w² = 9 → w = √9 → w = 3
3w = 3 · 3 = 9
width = 3
length = 9
The perimeter:
P = 2 · width + 2 · length
P = 2 · 3 + 2 · 9 = 6 + 18 = 24 ft.
Parameterize the lateral face

of the cylinder by

where

and

, and parameterize the disks

as


where

and

.
The integral along the surface of the cylinder (with outward/positive orientation) is then




Based on the shaded region, the value of x which makes this region a gnomon is x = 1.
<h3>What is value of x?</h3>
Based on the dimensions of the side that isn't shaded, and the dimensions of the side that is shaded, the value of x can be found as:
3/ 6 = (1 + 3) / (x + 6 + x)
1/2 = 4 / (6 + 2x)
6 + 2x = 4 / (1/2)
2x = 8 - 6
x = 2/2
x = 1
Find out more on shaded regions at brainly.com/question/9767762.
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