The base of a pyramid is an equilateral triangle of side 1 m. If the height of the pyramid is 4 metres, then… · ABC26GN5062
Subject: General Aptitude · Chapter: Volume and Surface Area
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)$0.550 \mathrm{m}^{3}$
(b)$0.577 \mathrm{m}^{3}$
(c)$0.678 \mathrm{m}^{3}$
(d)$0.750 \mathrm{m}^{3}$
Answer
Explanation
Area of the base $=\left(\frac{\sqrt{3}}{4} \times 1^{2}\right) \mathrm{m}^{2}=\frac{\sqrt{3}}{4} \mathrm{m}^{2}$. $$\begin{aligned} \therefore \text { Volume of pyramid } & =\left(\frac{1}{3} \times \frac{\sqrt{3}}{4} \times 4\right) \mathrm{m}^{3}=\left(\frac{\sqrt{3}}{3}\right) \mathrm{m}^{3} \\ & =\left(\frac{1.732}{3}\right) \mathrm{m}^{3}=0.577 \mathrm{m}^{3} . \end{aligned}$$
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