A right circular cylinder of radius r and height 2r exactly encloses a sphere of radius r. A famous result of Archimedes says the curved surface of the cylinder equals the surface area of the sphere. Verify by finding the cylinder's curved surface area in terms of π and r.

Question

Accepted Answer

4*π*r^2. Cylinder CSA = 2*π*r*h = 2*π*r*(2r) = 4*π*r^2, which equals the sphere's surface area 4*π*r^2.

A right circular cylinder of radius $r$ and height $2 r$ exactly encloses a sphere of radius $r$ .
A famous result of Archimedes says the curved surface of the cylinder equals the surface area of the sphere.
Verify by finding the cylinder's curved surface area in terms of π and $r$ .

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More Class 9 Surface Area of a Sphere practice

A right circular cylinder of radius r and height 2r exactly encloses a sphere of radius r.A famous result of Archimedes says the curved surface of the cylinder equals the surface area of the sphere.Verify by finding the cylinder's curved surface area in terms of π and r.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 9 Surface Area of a Sphere practice

A right circular cylinder of radius $r$ and height $2 r$ exactly encloses a sphere of radius $r$ .
A famous result of Archimedes says the curved surface of the cylinder equals the surface area of the sphere.
Verify by finding the cylinder's curved surface area in terms of π and $r$ .