IGCSE Mathematics Paper-1: Specimen Questions with Answers 98 - 100 of 324
Question 98
Describe in Detail
Essay▾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 =
Question 99
Write in Short
Short Answer▾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:
Question 100
Write in Short
Short Answer▾Solve
Explanation
Here, equation is
- So, now multiply 4 with the terms inside the brackets:
- Now, simplify as: .