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Calculate the volume of the regular three dimensional fig...

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

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 $^3$

View answer & explanation

Correct answer is D

|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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