Question

What’s the perimeter and surface area of this shape?
Please also show working out.

Answer 1

Answer: Perimeter = 8π ≈ 25.12

Area = 12π ≈ 37.68

Explanation:

This is a composite of two figures.

The bigger figure is a quarter-circle with radius (r) = 8 cm

The smaller figure is a quarter-circle with diameter = 8 cm --> r = 4

Perimeter of a quarter-circle =
`(1)/(4)(2\pi r)` =
`(\pi r)/(2)`

Perimeter of composite figure = bigger - smaller figure

`P_(bigger)=2\pi(8)\quad = 16\pi\\P_(smaller)=2\pi(4)\quad =8\pi\\P_(composite)=16\pi-8\pi \\.\qquad \qquad = \large\boxed{8\pi}`

Area of a quarter-circle =
`(1)/(4)\pi r^2`

`A_(bigger)=(1)/(4)\pi (8)^2\quad =16\pi\\\\A_(smaller)=(1)/(4)\pi (4)^2\quad =4\pi\\\\A_(composite)=16\pi-4\pi\\.\qquad \qquad = \large\boxed{12\pi}`