Solve system of inequalities graphically
The diagram shows a sphere with center O and a radius of 6 inches that has been cut by a plane. The cross-section formed by the
plane is shaded.
Which shape is a possible representation of the cross-section?
Which shape is a possible representation of the cross-section?
2 answers:
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Part 1:
Given that the length of the chord is 18 cm and the chord is midway the radius of the circle.
Thus, half the angle formed by the chord at the centre of the circle is given by:
Now,
Therefore, the radius of the circle is 10.4 cm to 1 d.p.
Part 2I:
Given that the radius of the circle is 10 cm and the length of chord AB is 8 cm. Thus, half the length of the chord is 4cm. Let the distance of the mid-point O to /AB/ be x and half the angle formed by the chord at the centre of the circle be θ, then
Now,
Part 2II:
Given that the radius of the circle is 10cm and the angle distended is 80 degrees. Let half the length of chord CD be y, then:
Thus, the length of chord CD = 2(6.428) = 12.856 which is approximately 12.9 cm.
Given that the length of the chord is 18 cm and the chord is midway the radius of the circle.
Thus, half the angle formed by the chord at the centre of the circle is given by:
Now,
Therefore, the radius of the circle is 10.4 cm to 1 d.p.
Part 2I:
Given that the radius of the circle is 10 cm and the length of chord AB is 8 cm. Thus, half the length of the chord is 4cm. Let the distance of the mid-point O to /AB/ be x and half the angle formed by the chord at the centre of the circle be θ, then
Now,
Part 2II:
Given that the radius of the circle is 10cm and the angle distended is 80 degrees. Let half the length of chord CD be y, then:
Thus, the length of chord CD = 2(6.428) = 12.856 which is approximately 12.9 cm.