# Conical area

A right angled triangle has sides a=12 and b=19 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation.

Result

V =  2422.438
S =  988.1

#### Solution:

$a = 12 \ \\ b = 19 \ \\ c = \sqrt{ a^2+b^2 } = \sqrt{ 12^2+19^2 } = \sqrt{ 505 } \doteq 22.4722 \ \\ c_{ 1 } = a^2/c = 12^2/22.4722 \doteq 6.4079 \ \\ c_{ 2 } = b^2/c = 19^2/22.4722 \doteq 16.0643 \ \\ h = \sqrt{ c_{ 1 } \cdot \ c_{ 2 } } = \sqrt{ 6.4079 \cdot \ 16.0643 } \doteq 10.1459 \ \\ S_{ 1 } = \pi \cdot \ h^2 = 3.1416 \cdot \ 10.1459^2 \doteq 323.3912 \ \\ V = (c_{ 1 }+c_{ 2 }) \cdot \ S_{ 1 }/3 = (6.4079+16.0643) \cdot \ 323.3912/3 \doteq 2422.4377 = 2422.438$
$S = \pi \cdot \ h \cdot \ (a+b) = 3.1416 \cdot \ 10.1459 \cdot \ (12+19) \doteq 988.0996 = 988.1$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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