Question

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

Answer 1

41.24 cm²

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
`3\ cm* 3\ cm`

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=
`length* width`

Area of rectangle=
`3\ cm* 3\ cm= 9\ cm^(2)`

∴ Area of rectangle= 9 cm²

Now, finding the area of circle.

Formula: Area of circle=
`\pi r^(2)` (∵ r is radius)

Area of circle=
`3.14* 4^(2) = 3.14* 16`

∴ Area of circle= 50.24 cm²

Next solving to find area of shaded region.

Area of shared region=
`\textrm{Area of the circle} - \textrm{Area of the rectangle}`

Area of shaded region=
`50.24\ cm^(2) - 9\ cm^(2) = 41.24\ cm^(2)`

∴ Area of shaded region= 41.24 cm²