WAEC Mathematics Past Questions & Answers - Page 53

261.

If the total surface area of a solid hemisphere is equal to its volume, find the radius

A.

3.0cm

B.

4.5cm

C.

5.0cm

D.

9.0cm

Correct answer is B

T.S.A of hemisphere = 3\(\pi r^2\)

vol of hemisphere = \(\frac{2}{3} \pi r^3\)

3\(\pi r^2\) = \(\frac{2}{3} \pi r^3\)

3 = \(\frac{2}{3}r\)

9 = 2r

r = \(\frac{9}{2}\)

r = 4.5cm

262.

The dimensions of water tank are 13cm, 10cm and 70cm. If it is half-filled with water, calculate the volume of water in litres

A.

4.55 litres

B.

7.50 litres

C.

8.10 litres

D.

9.55 litres

Correct answer is A

Vol of a cubiod = L x b x h

v = 13cm  x 10cm x 70cm

= 9100cm

Since it is half-filled = \(\frac{9100}{2}\)cm

= 4550cm

4550cm \(\to\) 4.55 litres

263.

Water flows out of a pipe at a rate of 40\(\pi cm^2\) per seconds into an empty cylinder container of base radius 4cm. Find the height of water in the container after 4 seconds.

A.

10 cm

B.

14 cm

C.

16 cm

D.

20 cm

Correct answer is A

Volume of a cylinder = \(\pi r^2h\)

40\(\pi cm^3\) = \(\pi. 4^2h\)

40\(cm^3\) = 16h

h = 2.5cm/sec

In 4 seconds, 2.5cm x 4

= 10cm

264.

An arc of a circle of radius 7.5cm is 7.5cm  long. Find, correct to the nearest degree, the angle which the arc subtends at the centre of the circle. [Take \(\pi = \frac{22}{7}\)]

A.

29\(^o\)

B.

57\(^o\)

C.

65\(^o\)

D.

115\(^o\)

Correct answer is B

lac = \(\frac{\theta}{360}\) x 2\(\pi\)r

7.5 = \(\frac{\theta}{360}\) x 2 x \(\frac{22}{7}\) x 7.5

7.5 = \(\frac{330\theta}{2520}\)

\(\theta\) = \(\frac{7.5}{0.1309}\)

\(\theta\) = 57.29

\(\theta\) = 57 \(^o\)

265.

Simplify; 3x - (p - x) - (r - p)

A.

2x - r

B.

2x + r

C.

4x - r

D.

2x - 2p - r

Correct answer is C

3x - (p - x) - ( r - p) = 3x - p + x - r + p = 4x - r