The total surface area of a cuboid is 214cm^ . if l = 7 , b=6 , find height (h) =?
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mysticd
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Hi ,
Let dimensions of the cuboid is ,
length = l units
breadth = b units
height = h units
Total surface area = 214 square units
2( lb + lh + bh ) = 214
lb + lh + bh = 107 ----( 1 )
volume = 210
lbh = 210 -----( 2 )
base area = 42
lb = 42 ------ ( 3 )
divide ( 2 ) with equation ( 3 ) , we get
h = 5 ---( 4 )
put value of h and lb = 42 in equation ( 1 ),
42 + 5b + 5l = 107
5b + 5l = 107 - 42
5( b + l ) = 65
l + b = 13 ----( 5 )
( l - b )² = ( l + b )² - 4lb
= ( 13 )² - 4 × 42
= 169 - 168
= 1
l - b = √1
l - b = 1 ------ ( 6 )
solveing equations ( 5 ) and ( 6 ) , we get
l = 7 , b = 6
Therefore ,
required dimensions of the cuboid is
l = 7 units ,
b = 6 units ,
h = 5 units
I hope this helps you.
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Answer:
Given,
Total surface area = 214cm²
l = 7
b = 6
let height be h
formula for total surface area of cuboid = 2(lb +bh +hl)
214 = 2(7x6 + 6xh + hx7)
214 = 2(42 + 6h + 7h)
214 = 2(42 + 13h)
214 = 84 + 26h
214 - 84 = 26h
26h = 130
h = 130/26
h = 5
hence, the height is 5cm