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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) = $straight pi$ r²h
Surface Area (SA) = 2 $straight pi$ rh = 2 $straight pi$ r²

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

1 : 3
2 : 3
1 : 1
3 : 2

hint 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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