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
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
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)]
Source: Myschool Past Questions Archive (Record #32553)