Question

Luca is designing a propeller system that consists of 3 blades, each of which is identical. The blades are sectors of a circle that have radii of 4 inches and central angles of 20 . The blades are to be made from steel that weighs 16 grams per square inch. Determine the weight of the three blades together to the nearest gram.

Answer 1

Total weight of blades = ~134gm

Explanation:

Radius of circle,
`r` = 4 inches

Central angle of sector =
`20^\circ`

For finding the weight of blades, we need to find the area of blades.

Area of circle, A =
`\pi r^(2)`

We know that circle has a central angle of
`360^\circ`.

We can use unitary method to find the area of sector with angle
`20^\circ`.

Area of
`360^\circ` central angle =
`\pi r^(2)`

Area of
`1^\circ` central angle =
`(\pi)/(360) r^(2)`

Area of
`20^\circ` central angle =
`(\pi)/(360) r^(2) * 20`

Putting value of r = 4 inches

Area of blade:

`(\pi)/(360) * 4^(2) * 20\\\Rightarrow 2.79\ in^(2)`

We have 3 blades here, so area of 3 blades =

`2.79 * 3\\\Rightarrow 8.38\ in^(2)`

Weight of steel = 16 grams per square inch

Total weight of all 3 blades = 16
`*` 8.38 = ~ 134gm