Calculate the volume of the regular three-dimensional figure drawn above, where < ABC = 90° (a right-angled triangle).

  • A 394 cm\(^3\)
  • B 425 cm\(^3\)
  • C 268 cm\(^3\)
  • D 540 cm\(^3\)
jamb 2019mathematics

The correct answer is D. 540 cm\(^3\)

|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\(^3\)

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