Practice | Hashtable

1. The base of a pyramid is an equilateral triangle of side 1 m. If the height of the pyramid is 4 metres, then the volume is :

A. 0.550 m³

B. 0.577 m³

C. 0.678 m³

D. 0.750 m³

Solution:

Area of the base :

\begin{aligned} = (\frac{\sqrt{3}}{4} \times 1^{2}) m^{2} \\ = \frac{\sqrt{3}}{4} m^{2} \end{aligned}

∴ Volume of pyramid :

\begin{aligned} = (\frac{1}{3} \times \frac{\sqrt{3}}{4} \times 4) m^{3} \\ = (\frac{\sqrt{3}}{3}) m^{3} \\ = (\frac{1.732}{3}) m^{3} \\ = 0.577 m^{3} \end{aligned}

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