# The conical

The conical candle has a base diameter of 20 cm and a side of 30 cm. How much dm ^ 3 of wax was needed to make it?

Result

V =  2.962 dm3

#### Solution:

$D=20 \ \text{cm} \ \\ s=30 \ \text{cm} \ \\ \ \\ r=D/2=20/2=10 \ \text{cm} \ \\ h=\sqrt{ s^2-r^2 }=\sqrt{ 30^2-10^2 } \doteq 20 \ \sqrt{ 2 } \ \text{cm} \doteq 28.2843 \ \text{cm} \ \\ \ \\ V_{1}=\dfrac{ 1 }{ 3 } \cdot \ \pi \cdot \ r^2 \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 3.1416 \cdot \ 10^2 \cdot \ 28.2843 \doteq 2961.922 \ \text{cm}^3 \ \\ \ \\ V=V_{1} \rightarrow dm^3=V_{1} / 1000 \ dm^3=2961.92195878 / 1000 \ dm^3=2.96192 \ dm^3=2.962 \ \text{dm}^3$

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