The base of a right pyramid is an equilateral triangle each side of which is 2m long. Every slant edge
is 3m long. Then volume of pyramid is:??
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Ans:
=4√59 cm ³
3
each side of the base,
a=4 cm
slant edge,
s=5 cm
Let height of the pyramid =h cm
height of the base
hb= √3a
2
radius of the circumcircle of the base (whose center will be the centroid)
r=2hb3=23×√3a
2
=a√3
Using Pythagorean theorem,
r2+h2=s2(a√3)
2
h2=s2a23+h2
=
s
2
4
2
3
+
h
2
=
5
2
16
3
+
h
2
=
25
h
2
=
59
3
Base area,
A
=
√
3
a
2
4
=
√
3
×
4
2
4
=
4
√
3
volume of pyramid
=
1
3
A
h
=
1
3
×
4
√
3
×
√
59
3
=
1
3
×
4
√
3
×
√
59
√
3
=
4
√
59
3
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