In the diagram, the radius of the outer circle is 2x cm and the radius of the inside circle is 6 cm. The area of the shaded region is 288π cm2. What is the value of x?
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18 cm
Step-by-step explanation:
Area of the shaded region = Area of the larger circle - Area of the smaller circle.
Area of a circle = pie × r²
Area of smaller circle = 6² × pie = 36pie
Area of larger circle = (2x)² × pie = 4x²Pie.
4x² pie - 36 pie = 288 pie
Divide through by 4 pie we have :
x² - 9 = 72
x² = 72 + 9
x² = 81
Getting square root of both sides we have :
x = 9 cm
The value of x is therefore 9.
The radius of the large circle = 9 × 2 = 18 cm
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