Question

Lionel created a picture to hang on his wall. The drawing is below. Each circle has a radius of 8cm. The circles touch each other and the ends of the canvas. The background of Lionel’s picture is black. What is the area of the black portion?

Answer 1

219.7522cm^2

Explanation:

To find area of black portion, we will find the area of the whole square first.

Length of square = 4xRadius of circle

= 4 x 8cm

= 32cm

Area of Square = Length x Width = 32x32

=
`1024cm^(2)`

Now we find the area of the 4 circles.

Area of 4 circles = 4 x Area of circle

=
`4\pi r^(2)`

=
`4\pi (8)^(2) \\=4\pi (64)\\=256\pi cm^(2)`

Area of black portion = Area of square - Area of 4 circles

=
`1024cm^(2) -256\pi cm^(2)`

=
`219.7522cm^(2)`