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?
A. 28cm2 B. 42cm2 C. 70cm2 D. 84cm2
Correct Answer: 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\(^3\)
