CIE Mathematics Paper-1: Specimen Questions 98 - 99 of 175

Question number: 98

Essay Question▾

Describe in Detail

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

A cylinder having a triangle in it - XYZ

A cylinder having a triangle in it - XYZ

Find the given calculations by using the appropriate formulas of cylinder and triangle

(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, XYZisrightangledtriangle.

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

So, using cosine formula,

tanθ=YZXY=614=0.43θ=tan10.43θ=23.270 .

(b) Length of diagonal XZ:

Here, XYZisrightangledtriangle.

So, formula for sides: diagonal2(XZ2)=Side12(XY2)+Side22(YZ2) , where XY = 14 cm and YZ = 6 cm is given,

XZ2=142+62=196+36=232XZ=15.23cm .

(C) Area of cylinder = 2πrh+2πr2 , where, height h = 14 cm and radius r = 6 cm.

So, area of cylinder = (2×3.14×6×14)+(2×3.14×62)=527.52+226.08=753.6cm2.

Question number: 99

Short Answer Question▾

Write in Short

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 parachute is at some height from ground

A parachute is at some height from ground

Find the below given calculations by using given distance

(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: c=a2+b2 , where a = 500 m and b = 800 m, c = XZ.

So, XZ=c=(500)2+(800)2=250000+640000=890000=943.4m.

(b) For angle XZY: sinZ=XYYZ=500800=0.625Z=sin1(0.625)Z=38.70

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