The given figure is of a solid square based pyramid. If the length of side of the base (BC) is 16cm and the length of the lateral edge (PD) is 2rootunder 41 cm ,find the volume of the pyramid.
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The given figure is of a solid square based pyramid. If the length of side of the base (BC) is 16cm and the length of the lateral edge (PD) is 2rootunder 41 cm ,find the volume of the pyramid.
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Step-by-step explanation:
(a) Since all the edges of a square pyramid are of length 12 cm, lateral faces of the pyramid are equilateral triangles having each edge of 12 cm.
Thus, area of one lateral face =
4
3
×12×12=36
3
sq.cm
(b) An edge =12 cm=a
Slant height =l=
2
3
×1=6
3
cm
Surface area of pyramid
=a
2
+4×
4
3
a
2
=12
2
+
4
3
×12
2
=144×144
3
=144(1+
3
)sq.cm
(c) Length of edge of pyramid, a=12 cm
New length of edge, a
′
=24 cm
New surface area of the pyramid
=(a
′
)
2
+4×
4
3
(a
′
)
2
=24
2
+4×
4
3
×24
2
=576+576
3
=576(1+
3
)sq.cm
Previous surface are, S=144(1+
3
)sq.cm
New surface area, S
′
=576(1+
3
)sq.cm
⇒S
′
=4S
Thus, if the length of the sides of the pyramid is doubled, the surface area will be 4 times the previous one
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