Axial cut of a rectangle

Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long.

Result

V =  3534.292 cm3
S =  1295.907 cm2

Solution:

D=15 cm u=25 cm  r=D/2=15/2=152=7.5 cm h=u2D2=252152=20 cm  S1=π r2=3.1416 7.52176.7146 cm2 V=S1 h=176.7146 203534.2917=3534.292 cm3D = 15 \ cm \ \\ u = 25 \ cm \ \\ \ \\ r = D/2 = 15/2 = \dfrac{ 15 }{ 2 } = 7.5 \ cm \ \\ h = \sqrt{ u^2 - D^2 } = \sqrt{ 25^2 - 15^2 } = 20 \ cm \ \\ \ \\ S_{ 1 } = \pi \cdot \ r^2 = 3.1416 \cdot \ 7.5^2 \doteq 176.7146 \ cm^2 \ \\ V = S_{ 1 } \cdot \ h = 176.7146 \cdot \ 20 \doteq 3534.2917 = 3534.292 \ cm^3
S=2π r h+2 S1=2 3.1416 7.5 20+2 176.71461295.907=1295.907 cm2S = 2 \pi \cdot \ r \cdot \ h + 2 \cdot \ S_{ 1 } = 2 \cdot \ 3.1416 \cdot \ 7.5 \cdot \ 20 + 2 \cdot \ 176.7146 \doteq 1295.907 = 1295.907 \ cm^2



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