Find the value of l in the frustrum above
Attached Figure / Diagram
A
5cm
B
6cm
C
7cm
D
8cm
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\DeltaABE and \DeltaACD are similar
therefore \(\frac{ x}{ x + 4} = \frac{3}{6}\)
6x = 3(x+4)
6x = 3x + 12
3x = 12
x = 4
In \DeltaACD; \(L^2\) = \((4+4)^2 + 6^2\)
= \(8^2 + 6^2\)
= 64 + 36
= 100
L = \(\sqrt{100}\)
= 10cm
In ABE, \((AE)^2 = 4^2 + 3^2\)
= 16 + 9
= 25
AE = 5cm
∴L = 10 - 5
= 5cm
Source: Myschool Past Questions Archive (Record #10418)