Question

Given a cylinder with a surface area of 60 units squared and a height of 7 units. Find the volume of a sphere that has the same size radius as the given cylinder. Please explain how you did it... :)

Answer 1

The surface area of the circular cylinder is 2* pi*r^2 + 2*pi*r*h = 2*pi*r^2 + 14*pi, = 60. Solve for r:
2*pi*(r^2 + 7) = 60
r^2 + 7 = 30/pi
r = sqrt(30/pi - 7) = sqrt[(30 - 7*pi)/pi] The volume of the sphere is
(4/3)*pi*r^3 = (4/3)*pi*[(30 - 7*pi)/pi)^(3/2).
That works out to a radius of approximately 5.43 units.

Answer 2

Actually, S = 2pi*r^2 + 2pi*r*h = 2pi*r*(r+h) = 2pi*r(r+7) = 60.
So r^2 + 7*r - (30/pi) = 0.

Answer 3

You'll get a nasty expression for the exact solution since you need to use the quadratic formula.

Answer 4

Now make the equation: (i would like to say that the above answer is incorrect because he forgot to type the radius for the area of upper and lower circle.)
2(pi)r * 7 + 2(pi)r^2 = 60 (which is total surface area)
Then you will have:(solve above)
30/pi=7r+r^2
Then you can solve it with quatratic equation. If not it will be more complicated.
Like this

By perfect sqare which is proof of quatratic equation :(a+b)^2=a^2+2ab+b^2
you can make (r) the subject:
\[r=\sqrt{30/\pi} -7/2\]
Then substitue the r into the equation 4/3 *pi * r^3
Done.
Please do the work following these steps. I cant calculate on my own because I don't want to.

Answer 5

The radius is about 1.169 units and the volume of the sphere is about 5.724 cubic units.