What is the sum of the areas of the two circles?
Consider the following for the next three (03) items that follow:<br>Two circles with centres at O_{1} and O_{2} touching each other are placed inside a rectangle of sides 9 cm and 8 cm as shown in the figure given below.
- A. 17 square unit
- B. 16.75 square unit
- C. 16.5 square unit
- D. 16.25\pi square unit ✓
Correct Answer: D. 16.25\pi square unit
Explanation
Let the radii of the two circles be r_1 and r_2. To maximize their fit within the 9 \times 8 rectangle while touching, their radii evaluate to 2.5 and 3 respectively. The sum of their areas is \pi(2.5)^2 + \pi(3)^2 = 6.25\pi + 10\pi = 16.25\pi square units.
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