The variable "x" equals 7
Refer to the attached image.
As we can observe ABCD is a square, whose corners that is A,B,C and D lie on the circle.
The diameter AC = 0.35 meter.
We have to find the side of square.
Let the measure of side of a square be 'l' meter
In triangle ABC,
By Pythagoras theorem, we get





So, l = 0.25 meter
Therefore, the measure of side of the square is 0.25 meter.
Given:
Lateral Area = π * r * (√h² + r²)
Lateral Area = 100 in² ; height = 5 in
I find it hard to derive the formula of r because of the radical sign. So, I'll just plug each radius to the formula to check confirm the given lateral area.
a) r = 1.52138 ⇒ LA = 24.98
b) r = 4.658 ⇒ LA = 100
c) r = 78 ⇒ LA = 19152.68
d) r = 6.7432 ⇒ LA = 177.84
The radius is B.) r = 4.658 inches