The height of cylinders A and B will be 11 feet and 16.5 feet.
What is the surface area of a right circular cylinder?
Let r be the radius and h be the height of the cylinder.
Then the surface area of the cylinder will be
SA = 2πrh square units
Cylinder A has a radius of 6 feet and a height that is 5.5 feet less than Cylinder B. Cylinder B's radius is 4 feet.
[tex]\rm r_A = 6 \ feet\\\\\rm h_B = 5.5 + h_A \\\\ r_B = 4 \ feet[/tex]
The surface area of cylinder A will be
SA = 2π × 6 × [tex]\rm h_A[/tex]
The surface area of cylinder B will be
SA = 2π × 4 × [tex]\rm h_B[/tex]
The cylinders have the same surface area. Then we have
2π × 4 × [tex]\rm h_B[/tex] = 2π × 6 × [tex]\rm h_A[/tex]
[tex]\rm 4 (5.5 + h_A ) = 6 h_A \\\\2h_A = 22\\\\h_A = 11[/tex]
Then the height of the cylinder B will be
[tex]\rm h_B = 5.5 + h_A \\\\h_B = 5.5 + 11\\\\h_B = 16.5[/tex]
The height of cylinders A and B will be 11 feet and 16.5 feet.
More about the surface area of the cylinder link is given below.
https://brainly.com/question/22074027
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