Mathematics

Question

A 3 cm by 3 cm rectangle sits inside a circle with radius of 4 cm

1 Answer

  • Answer:

    41.24 cm²

    Step-by-step explanation:

    Here is the complete question:  A 3 cm by 3 cm rectangle sits inside a circle with radius of 4 cm. What is the area of the shaded region?

    Given: measurement of rectangle is [tex]3\ cm\times 3\ cm[/tex]

              Radius of circle is 4 cm.

    We can find the area of shaded region by subtracting area of rectangle from area of circle.

    First, lets find the area of rectangle

    Formula; Area of rectangle= [tex]length\times width[/tex]

    Area of rectangle= [tex]3\ cm\times 3\ cm= 9\ cm^{2}[/tex]

    Area of rectangle= 9 cm²

    Now, finding the area of circle.

    Formula: Area of circle= [tex]\pi r^{2}[/tex] (∵ r is radius)

    Area of circle= [tex]3.14\times 4^{2} = 3.14\times 16[/tex]

    Area of circle= 50.24 cm²

    Next solving to find area of shaded region.

    Area of shared region= [tex]\textrm{Area of the circle} - \textrm{Area of the rectangle}[/tex]

    Area of shaded region= [tex]50.24\ cm^{2} - 9\ cm^{2} = 41.24\ cm^{2}[/tex]

    Area of shaded region= 41.24 cm²