The diagram shows a sector of a circle with centre $$$O$$$, radius $$$8 \mathrm{~cm}$$$ and sector angle $$$165^{\circ}$$$. The surface area of a sphere is the same as the area of the sector. Calculate the radius of the sphere. [The surface area, $$$A$$$, of a sphere with radius $$$r$$$ is $$$A=4 \pi r^{2}$$$.] ........................................ $$$\mathrm{cm}$$$

Mathematics

IGCSE&ALevel

CAIE

Exam No：0580_s20_qp_41 Year：2020 Question No：9(b)

Answer:

$2.71$ or $2.708 \ldots$

Knowledge points:

E5.3.1 Carry out calculations involving the circumference and area of a circle. (Answers may be asked for in multiples of π.)

E5.3.2 Solve problems involving the arc length and sector area as fractions of the circumference and area of a circle.

E5.4.1 Carry out calculations involving the surface area and volume of a cuboid, prism and cylinder. (Answers may be asked for in multiples of π.)

E5.4.2 Carry out calculations involving the surface area and volume of a sphere, pyramid and cone. (Formulae will be given for the surface area and volume of the sphere, pyramid and cone in the question.)

Answer:

Knowledge points:

Solution:

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