A cylnder with a height of 5cm, and a surface area of 100cm^2, what would be the radius?

Question

A cylnder with a height of 5cm, and a surface area of 100cm^2, what would be the radius. I also need to know how it is worked out. The steps taken in solving

Answer 1

surface area = (2 * pi * r^2) + (2 * pi * r * h)
h = 5, surface area = 100 (put in units later)

100 = (2 * pi * r^2) + (2 * pi * r * 5)
2pi*r^2 + 10pi*r - 100 = 0

Now bring in the best equation in the world. (Quadratic Formula)
x = (-b +- sqrt(b^2 - 4ac)) / 2a

r = (-10pi +- sqrt(100pi^2 + 800pi) / 4pi

Throw the negative out, because length cannot be negative.

r ~ 2.21cm

Answer 2

If the surface of the cylinder is 100 centimeter square and its height is 5 centimeters, we have the two required given to find the radius of the cylinder.

Thus, if we visualize the two given values as a parallelogram with height (H = 5) and area “A= 100) we can find the length of the parallelogram (L) by using the formula A = H x L where “A” stands for area.

Now, solving this equation for “L”, we have L = A/H = 100/5 = 20. Therefore, the circumference (P) of the cylinder is 20 centimeters. So, P = 20

We do have now what is needed to find the radius of the cylinder by using the familiar formula of P = 2πR, or 2πR = P, which translates into 2 x 3.14 x R = 20.
Solving now for R, we have …R = P/2π, which is R = 20/6.28 and therefore, R = 3.1847133, in close approximation.

Hope this helps

Answer 3

r is the radius
2 pi r is the circumference.
Circumference X Height = Surface area.
Circumference X 5 = 100
Circumference = 20
( pi = 22/7)
2 x 22/7 x r = 20
44/7 x r = 20
r = 20/44/7, = 7 x 20 / 44, = 140/44, = 3.18 cm.

Answer 4

area = 2 * r^2 * pi + 2r * pi * h
100 = 2r^2pi + 2r pi 5
50/pi = r^2 + 5r
r^2 + 5r - 50/pi = 0

now it's in quadratic formula... solve for r :) Only one of the 2 r's will make logical sense (one will more than likely be negative)

Best of luck!

Answer 5

If you are talking about the lateral surface are

S = 2pi * r * h
100 = 2pi * r * 5
100 = 10pi * r
r = 10/pi or about 3.1831cm

Answer 6

A=2*pi*r^2+2*pi*r*h
h=5
A=100
100=2*pi*r^2+2*pi*5*r
50=pi*r^2+5*pi *r
pi*r^2+5*pi*r-50=0
r=(-5*pi+sqrt(25*pi^2+50*4*pi))/2*pi note only +sqrt because a negative radius is impossible
r=-5/2+(1/2pi)29.58=-5/2+4.708=2.208cm