(a) The lake behind a dam has an area of 55 hectares. When the gates in the dam are open, water flows out at a rate of 75 000 litres per second. (i) Show that 90 million litres of water flows out in 20 minutes. (ii) Beneath the surface, the lake has vertical sides. Calculate the drop in the water level of the lake when the gates are open for 20 minutes. Give your answer in centimetres. (1 hectare = 104 m2, 1000 litres = 1 m?]​

a) The diagram shows a hemisphere with radius 6 cm.

Calculate the volume.

Give the units of your answer.

(The volume, V, of s sphere with radius r is V = 4/3πr³)

b). The diagram shows a prism ABCDEF.

The cross-section is a right angled triangle BCD. BD = 10 cm, BC = 5.2 cm and ED = 18 cm.

(i) a) Work out the volume of the Prism.

b) Calculate the angle BEC

c) The point G lies on the line ED and GD = 7 cm. Work out angle BGE

(Cambridge Assessment International Education. 0580/42, October/November 2019, Q 4)

(a)

(b)(i)a

(b)(i)b

(b)(i)c

2. The diagram shows a sector of a circle of radius 3.8 cm.

The arc length is 7.7 cm.

(i) Calculate the value of y.

(ii) Calculate the area of the sector.

(Cambridge Assessment International Education. 0580/42, May/June 2019, Q 8b)

(i)

(ii)

3

the expression (1.26)2t reveals the approximate rate of increases in the number of plants semiannually.

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