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 diameters □

A. 25
B. 36
C. 42
D. 48
E. 54
F. 66
G. 70

Answer 1

A,B,C,D,E

Explanation:

the relationship given between the area and circumference is:

`\text{Area} = 16 * \text{Circumference}`

Using the formulas for area and circumference of the circle

`\pi r^2 = 16(2\pi r)`

solving:

`r^2 = 32r`

`r = 32\,\text{units}`

convert this into diameter

`2r = d = 2(32)\,\text{units}`

`d = 64\,\text{units}`: Diameter of circle O

Now, the question is asking us to select all such diameters that can fit completely inside this circle O

So, all we need to do is just select all circles that have a diameter less than 64 units. All such circles that have a diameter less than 64 units will completely fit inside the circle O.

Hence, the circles that fit inside circle O are: A,B,C,D,E