Trying to find the height of a cylinder, given the following information?

Question

The surface area (including top) S of a cylinder having height h and base radius r is given by:
S=pi r(r+2h). Express h in terms of pi, r and S. Find h when: S=1.51m sq., pi=3.14, r=35.4cm.
Any answers would be appreciated.

Answer 1

First find the circumference: = Pi x Diameter

= 3.14 x 70.8 cm = 222.3 cm

Now: this figure is used as the base of a rectangle (an unfurled cylinder), which has an area of 1.51 m.sq. (This MUST be converted to cm.sq)

= 15100 cm.sq.

Now: Subtract the area of the top & bottom of the cylinder:

= 15100 - ((3.14 x 35.4) x 2) = 14877.7 cm.sq

Divide 14877.7 by 222.3 to give 66.9 cm as the height of the rectangle and therefore the height of the cylinder.

Answer 2

s= 2*pi*r^2+2*pi*r*h
2pi*rh=s - 2*pi*r^2
h = (s - 2pi*r^2)/2*pi*r = 32.52cm

(It is important to remember that the area "S" is given in meters and is equal to 15100 sq cm - convert to that before proceeding)

Answer 3

Should be 1.94m

Workings as follows:

1.51 / 2 x 3.14 x 0.354 x 0.354

Hope this is of some value

Answer 4

S = ¶r (r + 2h)

S/( ¶r ) = r + 2h

S/( ¶r ) - r = 2h

h = 1/2 (S/ ¶r - r)

h= 0.5 ( 1.51/(3.14 x 0.354) - 0.354)

h = 0.5 ( 1.358 - 0.354) = 0.502 m

Answer 5

on here pal no chance and pi =3.1401 isn't it

Answer 6

s = πr(r+2h)
r+2h = πr/s
2h = πr/s - r
h = πr/2s - r/2
h = (3.14x35.4) / (2x1.51) - 35.4/2
h = 19.1