+0  
 
0
25
1
avatar

The length of three unequal edges of a rectangular solid block are in G.P. The volume of the block is 216 cm^3 and the total surface area is 312 cm^2. The length of the longest edge is ?

 Jun 9, 2022
 #1
avatar+123309 
+1

a =  shortest edge

ar  = 2nd edge

ar^2 = longest edge

 

Volume  =   product of edge lengths....so....

 

216 = a^3 * r^3         take the cube root of both sides

 

6 =  ar

 

6/a = r

 

And for the surface area we have

 

312  =  2 [  a* ar  +  a* ar^2  + ar * ar^2 ] 

 

156  =   a * 6  +  a^2r^2  +  a^2 * r^2 * r  

 

156   =  6a + 36  +  36r

 

120 =  6a  + 36 ( 6/a)

 

20  = a  + 36/a

 

20a  = a^2  + 36

 

a^2  - 20a  + 36 =  0

 

(a - 18) ( a - 2)  = 0

 

The second factor set  =   0       gives us what we need for the shortest  side =  2

 

r = 6/a =  6/2 =  3

 

The longest  side  =    ar * r =   6 * 3 =   18 cm

 

cool cool cool

 Jun 9, 2022

6 Online Users