Find the radius of the base and the height of the cylinder if the total surface area is 12п and the height is 2 times the radius.

1. Let the radius of the base of the cylinder be r, and its height h. Then:

h = 2r.

2. The area of the base of the cylinder is equal to:

Sosn. = πr ^ 2.

3. Lateral surface area:

S side. = 2πrh.

4. Total surface area:

S = 2Sn. + S side .;
S = 2πr ^ 2 + 2πrh;
S = 2πr (r + h) = 12π;
r (r + h) = 6;
r (r + 2r) = 6;
3r ^ 2 = 6;
r ^ 2 = 2;
r = √2 (cm);
h = 2r = 2√2 (cm).
Answer:

cylinder base radius: √2 cm;
its height: 2√2 cm.