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A cuboid has a diagonal of length 9cm and a square base of side 4cm....

Mathematics
JAMB 1981

A cuboid has a diagonal of length 9cm and a square base of side 4cm. What is its height?

  • A. 9cm
  • B. \(\sqrt{65}\)cm
  • C. \(4\sqrt{2}\)cm
  • D. 7cm
  • E. 6.5cm
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Correct Answer: Option D
Explanation

The formula for calculating the diagonal of a cuboid is given by : \(\sqrt{l^2 + w^2 + h^2}\)

where w = width, l = length and h = height

9 = \(\sqrt{l^2 + w^2 + h^2}\)

81 = 4\(^2\) + 4\(^2\) + h\(^2\) 

81 - 16 - 16 =  h\(^2\) 

h\(^2\)  = 49

h = \(\sqrt{49}\) = 7cm

NOTE:[l = w = 4 (square base)]

 


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