MHB Did I Calculate the Perimeter of A Sector Correctly?

[mathdad]

A sector has the following:

radius = 5 inches

angle = 30°

I was told to use the formula in the picture.

My answer is P = 10.05 inches.

The book's answer is P = 12.62 inches.

Am I using the right formula?

View attachment 7891

 

[Joppy]

A sector has the following:

radius = 5 inches

angle = 30°

I was told to use the formula in the picture.

My answer is P = 10.05 inches.

The book's answer is P = 12.62 inches.

Am I using the right formula?

It looks like you have performed this computation: $(2 \pi / 360) (30)(2\pi / 360)(5) + (2)(5)$ instead of $(2 \pi / 360) (30)(5) + (2)(5)$

Remember: $\theta$ in degrees is equal to $\theta \cdot \dfrac{2\pi}{360}$ (or simply $\theta \cdot \dfrac{\pi}{180}$) in radians.

 

[mathdad]

I converted 30° to radians before using the formula. This was my error.

P = (30/360) • (2π)(5) + 2(5)

P = (1/12)((10π) + 10

P = 12.62 inches

I got it.