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=πr2h a=33 mm b=18 mm  r1=a/(2π) V1=πr12b  V1=182334π=850.84 mm3  r2=b/(2π) V2=πr22a   V2=332184π=1559.88 mm3  ΔV=V1V2=709 mm3V = \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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