Length of each edge of a regular tetrahedron is 1 cm. It volume is :
A. $$\frac{{\sqrt 3 }}{{12}}{\text{ }}c{m^3}$$
B. $$\frac{1}{4}\sqrt 3 {\text{ }}c{m^3}$$
C. $$\frac{{\sqrt 2 }}{6}{\text{ }}c{m^3}$$
D. $$\frac{1}{{12}}\sqrt 2 {\text{ }}c{m^3}$$
Answer: Option D
Solution(By Examveda Team)
Length of each edge of a regular tetrahedron = 1 cmVolume of regular tetrahedron :
$$\eqalign{ & = \frac{{{a^3}}}{{6\sqrt 2 }}{\text{ c}}{{\text{m}}^3} \cr & = \frac{1}{{6\sqrt 2 }} \cr & = \frac{{\sqrt 2 }}{{6\sqrt 2 \times \sqrt 2 }}{\text{ c}}{{\text{m}}^3} \cr & = \frac{{\sqrt 2 }}{{12}}{\text{ Or }}\frac{1}{{12}}\sqrt 2 {\text{ c}}{{\text{m}}^3} \cr} $$
Related Questions on Volume and Surface Area
A. 12$$\pi$$ cm3
B. 15$$\pi$$ cm3
C. 16$$\pi$$ cm3
D. 20$$\pi$$ cm3
In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
A. 75 cu. m
B. 750 cu. m
C. 7500 cu. m
D. 75000 cu. m
A. 84 meters
B. 90 meters
C. 168 meters
D. 336 meters
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