ABC26GN5066 · Volume and Surface Area
Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
Length of each edge, of a regular tetrahedron is 1 cm. Its volume is [SSC-CHSL (10+2) Exam, 2015]
(a)$\frac{\sqrt{3}}{12} \mathrm{cm}^{3}$
(b)$\frac{1}{4} \sqrt{3} \mathrm{cm}^{3}$
(c)$\frac{\sqrt{2}}{6} \mathrm{cm}^{3}$
(d)$\frac{1}{12} \sqrt{2} \mathrm{cm}^{3}$
Answer
Explanation
Length of each edge of a regular tetrahedron $$=1 \mathrm{cm}$$ Volume of regular tetrahedron $$\begin{aligned} & =\frac{a^{3}}{6 \sqrt{2}} \mathrm{cm}^{3} \\ & =\frac{1}{6 \sqrt{2}}=\frac{\sqrt{2}}{6 \sqrt{2} \times \sqrt{2}} \mathrm{cu} . \mathrm{cm} \\ & =\frac{\sqrt{2}}{12} \mathrm{cu} . \mathrm{cm} . \end{aligned}$$
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