Question

Hi there,
I need help to solve the perimeter and the surface area of this shape.
Thanks!

Answer 1

Answer: Perimeter = 6π ≈ 18.84

Area = 15π ≈ 47.10

Explanation:

This is a composite of a big semicircle with diameter of 10 --> radius (r) = 5

plus a medium semicircle with diameter of 6 --> r = 3

minus a small semicircle with diameter of 4 --> r = 2

Perimeter of a semicircle =
`(1)/(2)(2\pi r)=\pi r`

`P_(big)=\pi (5)\quad =5\pi\\P_(medium)=\pi (3)\quad =3\pi\\P_(small)=\pi (2)\quad =2\pi\\P_(composite) =5\pi+3\pi -2\pi\\.\qquad \qquad =\large\boxed{6\pi}`

Area of a semicircle =
`(1)/(2)(\pi r^2)`

`A_(big)=(1)/(2)\pi (5)^2\quad =12.5\pi\\\\A_(medium)=(1)/(2)\pi (3)^2\quad =4.5\pi\\\\A_(small)=(1)/(2)\pi (2)^2\quad =2\pi\\\\A_(composite) =12.5\pi+4.5\pi -2\pi\\\\.\qquad \qquad =\large\boxed{15\pi}`