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1 Pure Mathematics

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Question 115

A designer is creating a specialized acoustic panel. The panel ABCDA ABCDA\,ABCDA consists of a major sector ACBA ACBA\,ACBA of a circle with centre C C\,C and radius 10 cm, and a triangular region ACDACDACD, as shown in the geometry below. The point D D\,D lies on the radius CBCBCB. The radius of the circle is 10 cm, the length of AD AD\,AD is 9 cm and the angle ACD ACD\,ACD is 0.8 radians0.8\text{ radians}0.8 radians.

Diagram of panel ABCDA formed from a major sector with centre C and triangle ACD, where D lies on radius CB, AC is 10 cm, AD is 9 cm and angle ACD is 0.8 radians.

a.

Find the area of the major sector ACBAACBAACBA, giving your answer to one decimal place.

[3]
b.

Given that the angle ADC ADC\,ADC is obtuse,

find the size of angle ADCADCADC, giving your answer to 3 decimal places.

[3]
c.

Hence find the perimeter of the panel ABCDAABCDAABCDA, giving your answer to one decimal place.

[4]

1 Pure Mathematics Questions

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1.1.3 Set theory language and symbols
1.1.4 Definition, domain and range of functions