the ares of three adjacent faces of cuboids are 108cm square, 72 cm square and 96 cm square respectively. find the volume of cuboid.also find the dimensions of cuboid
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Its too long...
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Areas of three adjacent faces are given. let
lh = 108 cm²
⇒ l = 108/h
bh = 72 cm²
⇒ b = 72/h
lb = 96cm²
⇒ (108/h) × (72/h) = 96
⇒ (108×72)/h² = 96
⇒ h² = (108×72)/96
⇒ h² = 81
⇒ h = √81 = 9cm
h = 9cm
l = 108/9 = 12cm
b = 72/9 = 8cm
volume = lbh = 12×8×9 = 864cm³
lh = 108 cm²
⇒ l = 108/h
bh = 72 cm²
⇒ b = 72/h
lb = 96cm²
⇒ (108/h) × (72/h) = 96
⇒ (108×72)/h² = 96
⇒ h² = (108×72)/96
⇒ h² = 81
⇒ h = √81 = 9cm
h = 9cm
l = 108/9 = 12cm
b = 72/9 = 8cm
volume = lbh = 12×8×9 = 864cm³
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