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.

Correct 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 20=3534.292 cm3D=15 \ \text{cm} \ \\ u=25 \ \text{cm} \ \\ \ \\ r=D/2=15/2=\dfrac{ 15 }{ 2 }=7.5 \ \text{cm} \ \\ h=\sqrt{ u^2 - D^2 }=\sqrt{ 25^2 - 15^2 }=20 \ \text{cm} \ \\ \ \\ S_{1}=\pi \cdot \ r^2=3.1416 \cdot \ 7.5^2 \doteq 176.7146 \ \text{cm}^2 \ \\ V=S_{1} \cdot \ h=176.7146 \cdot \ 20=3534.292 \ \text{cm}^3
S=2π r h+2 S1=2 3.1416 7.5 20+2 176.7146=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=1295.907 \ \text{cm}^2



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