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?
Attached Figure / Diagram
A
28cm2
B
42cm2
C
70cm2
D
84cm2
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
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\(^3\)
Source: Myschool Past Questions Archive (Record #26518)