Cylinders

Area of the side of two cylinders is same rectangle of 33 mm × 18 mm.

Which cylinder has a larger volume and by how much?

Result

Δ V =  709 mm3

Solution:

$V = \pi r^2 h \ \\ a = 33 \ mm \ \\ b = 18 \ mm \ \\ \ \\ r_1 = a/(2\cdot \pi) \ \\ V_1 = \pi r_1^2 b \ \\ \ \\ V_1 = \dfrac{ 18^2 \cdot 33 } { 4 \pi } = 850.84 \ mm^3 \ \\ \ \\ r_2 = b/(2\cdot \pi) \ \\ V_2 = \pi r_2^2 a \ \\ \ \\ \ \\ V_2 = \dfrac{ 33^2 \cdot 18 } { 4 \pi } = 1559.88 \ mm^3 \ \\ \ \\ \Delta V = | V_1 - V_2 | = 709 \ \text{mm}^3$

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