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Rahul Namawat

· started a discussion

· 1 Months ago

Height should be replaced by volume I think (Question: 186072.0 )

.

Question:
Each edge of a regular tetrahedron is 4 cm. Its volume (in cubic cm) is –
Options:
A) \(\cfrac{16 \sqrt{3}}{3}\) cm3
B) 16 \(\sqrt{3}\) cm3 
C) \(\cfrac{16 \sqrt{2}}{3}\) cm3
D) 16 \(\sqrt{2}\) cm3
Solution:
Ans: (c) 

volume  of the regular tetrahedron

= \({\sqrt{2} \over 12}\)a3 

= \(\frac{\sqrt{2}}{12}\) × 4 × 4 × 4cm3 

= \(\cfrac{16 \sqrt{2}}{3}\)  cm3 

Knowledge Expert

· commented

· 1 Months ago

Dear student,

Height of tetrahedron= a (Root 2/3)
Volume of tetrahedron in terms of height- (root 3) * h^3/8.
if we put h = a(Root 2/3)

Volume of tetrahedron = (root 2)/12 a^3
if we put a=4
volume = 16(root 2)/3 cm^3


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