# Cone container

Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package.

Result

S =  669.043 cm2

#### Solution:

$V = 1000 \ cm^3 \ \\ h = 12 \ cm \ \\ \ \\ V = \dfrac{ 1 }{ 3 } \pi r^2 \ h \ \\ r = \sqrt{ 3 \cdot \ V/h/\pi } = \sqrt{ 3 \cdot \ 1000/12/3.1416 } \doteq 8.9206 \ cm \ \\ \ \\ s = \sqrt{ r^2+h^2 } = \sqrt{ 8.9206^2+12^2 } \doteq 14.9525 \ cm \ \\ \ \\ S_{ 1 } = \pi \cdot \ r^2 = 3.1416 \cdot \ 8.9206^2 = 250 \ cm^2 \ \\ S_{ 2 } = \pi \cdot \ r \cdot \ s = 3.1416 \cdot \ 8.9206 \cdot \ 14.9525 \doteq 419.0434 \ cm^2 \ \\ S = S_{ 1 }+S_{ 2 } = 250+419.0434 \doteq 669.0434 = 669.043 \ cm^2$

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#### Following knowledge from mathematics are needed to solve this word math problem:

Tip: Our volume units converter will help you with the conversion of volume units. Pythagorean theorem is the base for the right triangle calculator.

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