WAEC Mathematics Past Questions & Answers - Page 212

1,056.

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 is B

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\(^3\)

1,057.

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 area of the cross-section?

A.

4cm2

B.

6cm2

C.

15cm2

D.

20cm2

Correct answer is B

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\(^2\)

1,058.

In the diagram, MN||PQ, |LM| = 3cm and |LP| = 4cm. If the area of ∆LMN is 18cm2, find the area of the quadrilateral MPQN

A.

3cm2

B.

6cm2

C.

14cm2

D.

24cm2

Correct answer is C

\(\frac{LM}{LP} = \frac{3}{4}\)

\(\frac{Area of LMN}{Area of LPQ} = \frac{3^2}{4^2}\)

Area of LPQ = \(\frac{16}{9}\times 18 = 32 cm^2\)

Area of quadrilateral MPQN = 32 – 18 = \(14 cm^2\)

1,059.

A sector of a circle radius 14 cm subtends an angle 135° at the center of the circle. What is the perimeter of the sector? Take \(\pi = \frac{22}{7}\)

A.

47cm

B.

61cm

C.

88cm

D.

231cm

Correct answer is B

Perimeter of the sector = \(2r + \frac{\theta}{360} \times 2\pi r\)

= \(2(14) + \frac{135}{360} \times 2 \times \frac{22}{7} \times 14\)

= \(28 + 33\)

= 61 cm

1,060.

A chord of length 30cm is 8cm away from the center of the circle. What is the radius of the circle? Take \(\pi =\frac{22}{7}\)

A.

16cm

B.

17cm

C.

18cm

D.

20cm

Correct answer is B

From the diagram
\(r^2 = B^2 + 15^2\\
= 64 + 225\\
r = \sqrt{289} = 17cm\)