the length of three unequal edges of a rectangular solid block are in Geometric progration . the volume of the block is 216 cm^3 and the total surface area is 252 cm^2 the the length of longest edge is........
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Asked on December 20, 2019 by
Nizam Castelino
The lengths of three unequal edges of rectangular solid block are in GP. The volume of the block is 216 cm
3
and the total surface area is 252 cm
2
. The length of longest edge is
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ANSWER
Let the three unequal lengths of the block be
r
A
,AandAr
the volume A
3
equals 216
⇒A
3
=216
⇒A=6
Also the total surface area =2(
r
A
2
+A
2
+A
2
r)
Hence 2(
r
A
2
+A
2
+A
2
r)=252
⇒
r
1
+1+r=
2A
2
252
=
72
252
=
2
7
⇒
r
1
+r=
2
5
⇒
r
1
+r=
2
1
+2
Hencer=2or
2
1
So the longest side= 6×2=12cm
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