A right circular cylinder just encloses a sphere of radius
\(r\).
Calculate the ratio of the curved surface area of the cylinder to the surface area of the sphere.
Radius of a sphere \(=\) \(r\) units
Surface area of a sphere \(=\) sq. units
Radius of a cylinder \(=\) \(r\) units
Height of the cylinder \(=\) Diameter of the sphere \(=\) \(2r\) units
Curved surface area of the cylinder \(=\) sq. units
\(=\) \(2 \pi r \times 2r\)
\(=\)
Ratio \(=\) \(\frac{\text{Surface area of a sphere}}{\text{Curved surface area of a cylinder}}\)
\(=\)
\(=\)
Therefore, the ratio of their surface areas is .
Answer variants:
\(3 : 1\)
\(4 \pi r^2\)
\(4 \pi r^2\)
\(3 \pi r^2\)
\(2 \pi r h\)
\(1 : 1\)