The total surface area of a cylinder is numerically the same as its volume. The radius of the cylinder is r cm, the height is h cm. Express h in terms of r.

Answer:

20) A

Total surface area of a cylinder = 2πrh + 2πr²
Volume of a cylinder = πr²h

Since they are numerically the same,

2πrh + 2πr² = πr²h

2πr (h + r) = πr²h

2 (h + r) = rh

2h + 2r = rh

2r = rh – 2h

2r = h (r – 2)

h = 2r ÷ (r – 2)