Question

A game has a circular playing area in which you must hit a ball into a circular hole. The area of the playing area is 16ft2. The hole has a diameter of 1 ft. What is the probability of hitting a ball into the circular hole?
Express your answer as a percentage rounded to the nearest tenth.

Answer 1

Answer:

$4.9\%$

Step-by-step explanation:

we know that

To find out the probability of hitting a ball into the circular hole, divide the area of the hole by the area of the playing area

Let

x ----> the area of the hole

y ----> the area of the playing game

so

$P=\frac{x}{y}$

we have

$y=16\ ft^2$

Find the area of the hole

The area of the circle (hole) is equal to

$A=\pi r^{2}$

we have

$r=1/2=0.5\ ft$ ----> the radius is half the diameter

assume

$\pi =3.14$

substitute

$A=(3.14)(0.5)^{2}$

$A=0.785\ ft^2$

Find the probability

$P=\frac{x}{y}$

we have

$x=0.785\ ft^2$

$y=16\ ft^2$

substitute

$P=\frac{0.785}{16}$

$P=0.0491$

Convert to percentage

$0.0491*100=4.91\%$

Round to the nearest tenth

$4.9\%$