IGCSE Mathematics Paper-1: Specimen Questions with Answers 98 - 100 of 324

In the diagram YZ is the radius of a cylinder base, XY is height. In triangle XYZ angle YXZ is .

(a) Find the angle YXZ.

(b) Calculate the length of diagonal XZ.

(c) Calculate the area of the cylinder.

Explanation

Here, YZ is the radius of a cylinder base, XY is height.

(a) Here,

XY = 14 cm and YZ = 6 cm is given,

So, using cosine formula,

.

(b) Length of diagonal XZ:

Here,

So, formula for sides: , where XY = 14 cm and YZ = 6 cm is given,

.

(C) Area of cylinder = , where, height h = 14 cm and radius r = 6 cm.

So, area of cylinder =

As shown in below figure, a parachute X is 500 meters vertically above a point Y on the ground. A boy stands at a point Z, which is 800 meters horizontally from Y.

(a) Calculate the distance, XZ, of the boy from the parachute.

(b) Calculate angle XZY.

Explanation

Here,

(a) Triangle XYZ is a right angled triangle, so by using formula of sides: , where a = 500 m and b = 800 m, c = XZ.

So,

(b) For angle XZY:

Solve

Explanation

Here, equation is

• So, now multiply 4 with the terms inside the brackets:

• Now, simplify as: .