Calculate the diameter of a cylinder

• Dec 10th 2013, 09:43 AM
civil
Calculate the diameter of a cylinder
Need to solve this but its hurting my head ...hehe

Calculate the diameter of a cylinder. The cylinder has a spherical top and a flat circular base .
The overall surface area is 2 M square.
The total height is 84 cm ... Thats it. I can solve for regular cylinder but with a spherical top im stuck....SA for sphere is 4 pi r square so half that and H= H-R but bit stuck any help welcome ...

Thanks
• Dec 10th 2013, 09:56 AM
HallsofIvy
Re: Calculate the diameter of a cylinder
So this isn't really a cylinder, it is a cyinder with a hemispherical top. The surface are of the cylindrical part, which you say you can find, is $\displaystyle 84\pi r^2$ approximately. The flat base is a disk with radius r so has area $\displaystyle \pi r^2$. The surface of a sphere of radius r is $\displaystyle 4\pi r^2$ so the hemisphere is $\displaystyle 2\pi r^2$. That is, the "overall surface area" is $\displaystyle 84\pi r^2+ \pi r^2+ 2\pi r^2= 87 \pi r^2= 2$ square meters. Solve for r, in meters.
• Dec 10th 2013, 10:28 AM
civil
Re: Calculate the diameter of a cylinder
Thanks for the post ..i have not explained properly .. I can solve for a normal cylinder to find r using quadratics , however this problem the overall height including the hemisphere is 84 cm ..therefore 84 pi r sq is wrong and so i cannot establish the radius ....more help required to establish the cylinder height ?
• Dec 10th 2013, 01:50 PM
HallsofIvy
Re: Calculate the diameter of a cylinder
Okay, then the height of the cylinder is 84- r. Put that in where I had 84 before.
• Dec 11th 2013, 03:32 PM
bjhopper
Re: Calculate the diameter of a cylinder
area of 1/2 sphere= 1/2pi d^2
area of cylinder =pi(d)(0.84 - d/2)
area of base= pi d^2/4