*Balmoral Software*

Solutions: 1

The total volume of the hemisphere and cylinder is V, where

The surface area of the hemisphere is S

V/π = (2/3)R ^{3}+ R^{2}h[1]

The lateral surface area of the cylinder is S

S _{h}/π = 2R^{2}[2]

The surface area of the cylinder base is S

S _{c}/π = 2Rh[3]

The above four quantities are integers by convention. From [1], [2] and [3], we have

S _{b}/π = R^{2}[4]

so R is rational. By [4], R

which reduces to

The numerator and denominator must have the same sign, so

[5]

2 < R < 9/2In the latter case, h = 2/3 by [5] but SR = 3 or R = 4

Copyright © 2019 Balmoral Software (http://www.balmoralsoftware.com). All rights reserved.