Answer:
r = 3cm
Step-by-step explanation:
Use the formula for the surface area of a cylinder and solve to obtain r=3cm
Hence radius of base is 3 cm of right circular cylinder.
The cylinder is known as a right circular cylinder when the axis (one of the rectangle's sides) is perpendicular to the radius ((r)). The base and top of the right circular cylinder are both round and parallel to one another. The general formula for the total surface area of a cylinder is T. S. A. =[tex]2\pi rh+2\pi r^{2} .[/tex]
Given total surface area of right circular cylinder =84[tex]\pi cm^{2}[/tex]
Using formula for right circular cyinder =.[tex]2\pi rh+2\pi r^{2} .[/tex]=84
and height=11 cm
[tex]2\pi r11+2\pi r^{2} =84.\pi[/tex]
⇒[tex]11r+ r^{2} =84/2[/tex]
⇒[tex]11r+ r^{2} =42[/tex]
⇒[tex]r^{2} +11r-42=0[/tex]
⇒r = [tex]\frac{-11+-\sqrt{11^{2}-4(1)42 } }{2}[/tex]
⇒r=[tex]\frac{-11+-17}{2}[/tex]
⇒r=3,-1
Hence radius of base is 3 cm as value can't be negative .
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