Danessa needs to compare the area of one large circle with a diameter of 8 to the total area of 2 smaller circles with a diameter one-half that of the large circle. Which statements about the areas are true? Select three options. The area of the large circle is 16 pi.

The area of one small circle is 4 pi.

The area of one small circle will be one-half of the area of the large circle.

The total area of the two small circles will equal that of the large circle.

The total area of the two small circles will be one-half of the area of the large circle.

=>The area of the larger circle is 16π

=>The area of 1 small circle is 4π

=>The total area of the two small circles will be one-half of the area of the large circle

Step-by-step explanation:

To find out which statements are true about the areas of the given circle, let's find out dimensions and areas of the 3 circles:

==>Large circle (A):

diameter = 8

radius (r) = ½ × 8 = 4

Area = πr² = π4² = 16π

Area of Circle A = 16π

==>Small circles (B and C):

Diameter of 1 small circle = ½ of diameter of big circle A

Therefore, d of small circles = ½×8 = 4

Radius of small circles = ½d = ½×4 = 2

Area of the 2 small circles = 2(πr²)

= 2(π2²)

= 2(π4)

Area of 2 small circles = 8π

Area of 1 small circle = 4π

From our calculation the statements that would be true are:

=>The area of the larger circle is 16π

=>The area of 1 small circle is 4π

=>The total area of the two small circles will be one-half of the area of the large circle (8π/16π = ½). I.e. area of 1 big circle is twice that of the total area of the 2 small circles (2 × 8π).

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step-by-step explanation: