Let the bottom radius be x cm; ; Because the surface area of a circle is equal to 1 rectangle plus two circles, and the length of a rectangle is the perimeter of the bottom, the rectangle is divided into two parts, one is the rectangle on the side of a cylinder, and the other is the area of two bottom circles, which is twice that of πX? ; The lateral area of the cylinder is the circumference of the bottom 2Xπ times the height of the cylinder 4; Let's list the equations (which are multiplication symbols). π is approximately equal to 3. 144 (2x π)-2x π? ﹦ 13 1.88; Get 2π(X? ﹢4x)﹦ 13 1.88； Do an x-ray ﹢4x﹦ 13 1.88÷6.28； x？ +4X+4-4 = 2 1； (X+2)？ =25; X=3

A: The bottom radius is 3 cm.

the second question

Let the bottom radius x; Then 2π x+4x (2xπ) = 314; Get 3 1.4X? =3 14; x？ = 10; x =√ 10； Under the root symbol; -√ 10; Bottom radius √ 10

6.28√ 10 times 4√ 10 is 249.6.

This is the knowledge point of grade three, binary linear equation, radical operation.