# Cone

Calculate volume and surface area of ​​the cone with a diameter of the base d = 15 cm and side of cone with the base has angle 52°.

Result

V =  565.5 cm3
S =  463.7 cm2

#### Solution:

$D = 15 \ cm \ \\ r = D/2 = 15/2 = \dfrac{ 15 }{ 2 } = 7.5 \ cm \ \\ S_{ 1 } = \pi \cdot \ r^2 = 3.1416 \cdot \ 7.5^2 \doteq 176.7146 \ cm^2 \ \\ A = 52 \ ^\circ \ \\ h = r \cdot \ \tan( (A \rightarrow rad) = r \cdot \ \tan( (A \cdot \ \dfrac{ \pi }{ 180 } \ ) = 9.59956224145 ) \ \\ V = \dfrac{ 1 }{ 3 } \cdot \ S_{ 1 } \cdot \ h = \dfrac{ 1 }{ 3 } \cdot \ 176.7146 \cdot \ 9.5996 \doteq 565.4609 = 565.5 \ cm^3$
$s = \sqrt{ h^2 + r^2 } = \sqrt{ 9.5996^2 + 7.5^2 } \doteq 12.182 \ cm \ \\ S = S_{ 1 } + \pi \cdot \ r \cdot \ s = 176.7146 + 3.1416 \cdot \ 7.5 \cdot \ 12.182 \doteq 463.7467 = 463.7 \ cm^2$

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

Pythagorean theorem is the base for the right triangle calculator. See also our trigonometric triangle calculator.

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