Question

The number of square units in the area of circle O is equal to 16 times the number of units in its circumference Which of the following are diameters of circles that could fit completely inside circle 0? Indicate all such diametersa) 25b) 36c) 42d) 48e) 54f) 66g) 70

Answer 1

The diameters of circles that could fit completely inside circle O are 25, 36, 42, 48 and 54.

Explanation:

The actual diameter of the circle:

`\pi r^(2) = 16 x \\2\pi r = x\\\\16(2\pi r)=16x\\\\32\pi r= \pi r^(2) \\\\(32\pi r)/(\pi r) = (\pi r^(2) \\)/(\pi r) \\\\r = 32`

Since the radius is equal to 32 units, the diameter is equal to 64 units.

Therefore, the diameters of circles that could fit completely inside circle O must be smaller than or equal to 64.