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WAEC Mathematics Past Questions & Answers - Page 211

1,051.

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 π=227

A.

47cm

B.

61cm

C.

88cm

D.

231cm

Correct answer is B

Perimeter of the sector = 2r+θ360×2πr

= 2(14)+135360×2×227×14

= 28+33

= 61 cm

1,052.

A chord of length 30cm is 8cm away from the center of the circle. What is the radius of the circle? Take π=227

A.

16cm

B.

17cm

C.

18cm

D.

20cm

Correct answer is B

From the diagram
r2=B2+152=64+225r=289=17cm

1,053.

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

A.

9πcm2

B.

15πcm2

C.

16πcm2

D.

20πcm2

Correct answer is B

Curved surface area or a cone =πrl
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

1,054.

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.

1,055.

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)