# Slant height

The slant height of cone is 5cm and the radius of its base is 3cm, find the volume of the cone

Correct result:

V =  37.699 cm3

#### Solution:

$s=5 \ \text{cm} \ \\ r=3 \ \text{cm} \ \\ \ \\ h=\sqrt{ s^2-r^2 }=\sqrt{ 5^2-3^2 }=4 \ \text{cm} \ \\ \ \\ S_{1}=\pi \cdot \ r^2=3.1416 \cdot \ 3^2 \doteq 28.2743 \ \text{cm}^2 \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ S_{1} \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 28.2743 \cdot \ 4=37.699 \ \text{cm}^3$

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