WAEC Mathematics Past Questions & Answers - Page 213

1,061.

The height of a right circular cone is 4cm. The radius of its base is 3cm. Find the curved surface area

A.

\(9\pi cm^2\)

B.

\(15\pi cm^2\)

C.

\(16\pi cm^2\)

D.

\(20\pi cm^2\)

Correct answer is B

Curved surface area or a cone \(=\pi rl\)
from the information \(l^2 = 4^2 + 3^2 = 16+9\\
l = \sqrt{25} = 5; ∴ C.S.A\hspace{1mm} = \frac{22}{7}\times 3 \times 5\\
Since \frac{22}{7}=\pi ∴ C.S.A\hspace{1mm} =\hspace{1mm}15\pi\)

1,062.

A right pyramid is on a square base of side 4cm. The slanting side of the pyramid is \(2\sqrt{3}\) cm. Calculate the volume of the pyramid

A.

\(5\frac{1}{3}cm^3\)

B.

\(10\frac{2}{3}cm^3\)

C.

\(16cm^3\)

D.

\(32cm^3\)

Correct answer is B

No explanation has been provided for this answer.

1,063.

In the diagram O is the center of the circle. Reflex angle XOY = 210° and the length of the minor arc is 5.5m. Find, correct to the nearest meter, the length of the major arc.

A.

8m

B.

9m

C.

10m

D.

13m

Correct answer is A

Given, Length of minor arc = 5.5m

Angle subtended by minor arc = 360° - 210° = 150°

\(\therefore 5.5 = \frac{150}{360} \times 2 \times \frac{22}{7} \times r \)

\(\frac{55r}{21} = 5.5\)

\(r = \frac{5.5 \times 21}{55}\)

r = 2.1m

Length of major arc = \(\frac{210}{360} \times 2 \times \frac{22}{7} \times 2.1\)

= \(7.7m \approxeq 8m\) (to the nearest metre)

1,064.

In the diagram, PQ is the diameter of the circle and ∠PRS = 58°. Find ∠STQ.

A.

29o

B.

32o

C.

42o

D.

53o

Correct answer is B

In \(\Delta\) PRQ, < SRQ = 90° - 58°

< SRQ = < QTS = x (angles in the segment)

\(\therefore\) x = 32°

1,065.

PQRS is a rhombus of side 16cm. The diagonal |QS| = 20cm. Calculate, correct to the nearest degree, ∠PQR

A.

51o

B.

64o

C.

77o

D.

103o

Correct answer is D

cos\(\alpha\) = \(\frac{10}{16}\) = 0.625

\(\alpha\) = cos-1(0.625)

= 51.3o

∠PQR = 2\(\alpha\)

= 2(51.3o)

= 102.6

= 103o