Calculate the volume of the regular three dimensional figure drawn above, where < ABC = 90^\circ (a right- angled triangle).
A
394 cm\(^3\)
B
425 cm\(^3\)
C
268 cm\(^3\)
D
540 cm\(^3\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
|AC| = |DF| = 13 cm
Using Pythagoras theorem,
|AC|\(^2\) = |AB|\(^2\) + |BC|\(^2\)
13\(^2\) = 12\(^2\) + |BC|\(^2\)
|BC|\(^2\) = 169 - 144 = 25
|BC| = \(\sqrt{25}\)
= 5 cm
Volume of triangular prism = \(\frac{1}{2} \times base \times length \times height\)
= \(\frac{1}{2} \times 5 \times 12 \times 18\)
= 540 cm\(^3\)
Source: Myschool Past Questions Archive (Record #55461)