# What is the total surface area of a cylinder whose radius equals 6cm and height equals 30cm?

A cylinder has 2 circular ends and the curved side.

If the cylinder was a drinks can, then it could be cut down from one ciircular end to the other and the side uncurled to give a rectangle with one dimension the height of the cylinder and the other the circumference of the circular end.

Thus the surface area of a cylinder is twice the area of an end plus the circumference of the end times the height of the cylinder:

area = 2{pi}r

= 2{pi}r(r + h)

= 2{pi}6(6 + 30)

= 12{pi}36

= 432{pi}

~= 1357.2 cm

If the cylinder was a drinks can, then it could be cut down from one ciircular end to the other and the side uncurled to give a rectangle with one dimension the height of the cylinder and the other the circumference of the circular end.

Thus the surface area of a cylinder is twice the area of an end plus the circumference of the end times the height of the cylinder:

area = 2{pi}r

^{2}+ 2{pi}rh= 2{pi}6(6 + 30)

= 12{pi}36

= 432{pi}

~= 1357.2 cm

^{2}