Respuesta :

duduburdfly

Answer: C) 56.4 ft^2

Step-by-step explanation:

The area of a circle is defined as  A= π x r^2

The first step will be finding the largest circles area as a whole.

We know that the two inner circles have equal diameters of 6 ft.

One diameter of the small circle is equal to the radius of the larger one.

So the radius of the large circle will be 6 ft.

So plug 6 into the equation.

A = π x 6^2

A is approximately equal to 113 ft^2.

This is not the answer however because we need to find the shaded region. We will do this by subtracting the areas of the two small inner circles from 113.

The area of the smaller inner circles will be:

A = π x 3^2

A = 28.3 ft^2

There are two of them however so we have to add their areas together.

28.3 + 28.3 = 56.6 ft^2

We now subtract the area of the white circles from the total area of the large circle.

113 - 56.5 = 56.4 ft^2

The single change in the tenths place likely came from rounding.

micahdisu

Answer: The correct answer is C; 56.5 ft^2

Step-by-step explanation: A careful observation shows that we have three (3) circles in the diagram. One big circle with two smaller circles inserted inside it.

One of the smaller circles has a radius of 3 ft. However note that the tiny strokes on the radii of both circles indicates that they are equal in measurement. Hence, both smaller circles each have a radius of 3 ft. Also, if we extend the radii of both smaller circles from end to end, what we would have is 3 + 3 + 3 + 3 and that equals 12. This is the diameter of the bigger circle. This gives the radius of the bigger circle as 6 ft (diameter/2).

At this point we can begin our calculations. The area of each smaller circle is given as

Area = pi x radius^2

(Please note that ^2 means squared, or raised to the power of 2)

Area = 3.14 x 3^2

Area = 3.14 x 9

Area = 28.26

Remember that we have two smaller circles with equal radius (3 ft)

Hence the area of both circles equals

28.26 x 2 and that equals 56.52 ft

In order to calculate the area of the bigger circle

Area = pi x radius^2

Area = 3.14 x 6^2

Area = 3.14 x 36

Area = 113.04

If the area of the entire larger circle is now known, we can subtract the area of the two smaller circles to help us arrive at the area of the shaded region. This can be expressed as;

Area of shaded region = 113.04 - 56.52

Area of shaded region = 56.52 and approximately this is equal to 56.5 ft

Otras preguntas