# Area of the cone

Calculate the surface area of the cone, you know the base diameter 25 cm and a height 40 cm.

Correct result:

S =  2136.583 cm2

#### Solution:

$D=25 \ \text{cm} \ \\ r=D/2=25/2=\dfrac{ 25 }{ 2 }=12.5 \ \text{cm} \ \\ h=40 \ \text{cm} \ \\ s=\sqrt{ h^2+r^2 }=\sqrt{ 40^2+12.5^2 } \doteq 41.9076 \ \text{cm} \ \\ S_{1}=\pi \cdot \ r^2=3.1416 \cdot \ 12.5^2 \doteq 490.8739 \ \text{cm}^2 \ \\ S_{2}=\pi \cdot \ r \cdot \ s=3.1416 \cdot \ 12.5 \cdot \ 41.9076 \doteq 1645.709 \ \text{cm}^2 \ \\ S=S_{1}+S_{2}=490.8739+1645.709=2136.583 \ \text{cm}^2$

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