Mathematics
Grade10
Easy

Question

An engineering firm wants to construct a cylindrical structure that will maximize the volume for a given surface area. The following formulas are given for the volume and surface area of cylinders.
Volume (v) = straight pir2h
Surface Area (SA) = 2straight pirh = 2straight pir2

calculate the ratio of volume for cylinder A to volume for cylinder B?

  1. 1 : 3
  2. 2 : 3 
  3. 1 : 1 
  4. 3 : 2

Hint:

To find the ratio of volume for cylinder A to volume for cylinder B, Find the volume of cylinders A and B then divide them in terms of r.

The correct answer is: 2 : 3


    Volume for cylinder A = πr2 h = πr2 (2r) = 2πr3
    Volume for cylinder B = πr2 h = πr2 (3r) = 3πr3
    straight V subscript straight A over straight V subscript straight B space equals space fraction numerator 2 πr cubed over denominator 3 πr cubed end fraction space equals space 2 over 3
    So, ratio of volume for cylinder A to volume for cylinder B is 2 : 3

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