Equilateral 81142

The rotating body was created by rotating an equilateral triangle with a side length of a=2 cm around one of its sides. Calculate the volume of this rotating body.

Correct answer:

V =  6.2832 cm³

Step-by-step explanation:

$$\begin{gathered} a=2\text{cm} \\ h=a/2=2/2=1\text{cm} \\ {a}^2=h^2+r^2 \\ r=\sqrt{a^2-h^2}=\sqrt{2^2-1^2}=\sqrt{3}\text{cm}\doteq 1.7321\text{cm} \\ {V}_1=\frac{1}{3}\cdot \pi \cdot r^2\cdot h=\frac{1}{3}\cdot 3.1416\cdot 1.7321^2\cdot 1\doteq 3.1416{\text{cm}}^3 \\ {V}_2=V_1=3.1416\doteq 3.1416{\text{cm}}^3 \\ V=V_1+V_2=3.1416+3.1416=6.2832{\text{cm}}^3 \end{gathered}$$

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