The diagram shows a triangular prism of length 7cm. The right – angled triangle PQR is a cross section of the prism |PR| = 5cm and |RQ| = 3cm. What is the volume of the prism?
- 28cm2
-
42cm2
- 70cm2
- 84cm2
The correct answer is: B
Explanation
Volume of prism = Area x height
In \(\Delta\) RQP, QR\(^2\) + QP\(^2\) = RP\(^2\)
3\(^2\) + QP\(^2\) = 5\(^2\)
QP\(^2\) = 5\(^2\) - 3\(^2\)
QP = \(\sqrt{16}\)
= 4 cm
\(\therefore\) Area = \(\frac{1}{2} \times base \times height\)
= \(\frac{1}{2} \times 3 \times 4\)
= 6 cm\(^2\)
Volume = 6 x 7
= 42 cm\(^3\)