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Rahul Patwa

· started a discussion

· 1 Months ago

solution (Question: 223399.0 )

solution

Question:
A pyramid on a square  base has four equilateral triangles on its four other faces, each edges being 10m. Find its volume.
Options:
A) 235.7 m3
B) 253.7 m3
C) 532.7 m3 
D) 352.7 m3
Solution:
Ans: (a) Let OABCD be the given pyramid which has   a square base (i.e. ABCD)

The four faces of the pyramid are 


equilateral triangles.

Since each edge = 10 m

 So,  AB = BC = DC = AD = 10 m

OA = OB = OC = OD = 10 m

Using the formula for pyramid 

Volume V; = \(\cfrac{1}{3}\) Ah

Where A = 10 ×10

and h = OX  = \(\sqrt{OZ^2 -XZ^2}\)

OZ = height of the equilateral \(\Delta\)OBC = \(\cfrac{\sqrt{3}}{2}\) ×10

= 5 \(\sqrt{3}\)

So, h = \(\sqrt{(5 \sqrt{3})^2 - 5^2}\)    = 5 \(\sqrt{2}\) 

\(\Rightarrow\) V = \(\cfrac{1}{3}\) ×100 × 5 \(\sqrt{2}\)

= 235.7 m3  

Hence, the volume of the pyramid is 235.7m3

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