Write True or False and justify your answer.
$A$ right circular cylinder just encloses a sphere of radius $r$ as shown in the figure. The surface area of the sphere is equal to the curved surface area of the cylinder.
$A$ right circular cylinder just encloses a sphere of radius $r$ as shown in the figure. The surface area of the sphere is equal to the curved surface area of the cylinder.
(TRUE) True.
Here,the radius of the sphere $=$ radius of the cylinder $= r$.
The diameter of the sphere $=$ height of the cylinder $= 2r$.
The surface area of the sphere $= 4 \pi r^2$.
The curved surface area of the cylinder $= 2 \pi r h = 2 \pi r (2r) = 4 \pi r^2$.
Since both areas are equal to $4 \pi r^2$,the statement is true.
Here,the radius of the sphere $=$ radius of the cylinder $= r$.
The diameter of the sphere $=$ height of the cylinder $= 2r$.
The surface area of the sphere $= 4 \pi r^2$.
The curved surface area of the cylinder $= 2 \pi r h = 2 \pi r (2r) = 4 \pi r^2$.
Since both areas are equal to $4 \pi r^2$,the statement is true.
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