Question

Rebecca is sharing a pizza with some friends. Below is an Image of how she cuts the pizza.

AE is a diameter of the 20 in pizza!
a) If rebecca wants the biggest piece which one would she choose ( name it by its arc)? Be careful the image may not be drawn to scale
b) Rebecca loves stuffed crust!! She decides to figure out the length of cheese in her piece of the crust ( hint find the arc length

Answer 1

a) The piece of pizza she should choose is BE

b) The length of the cheese in her piece of the crust is approximately 20.07 inches

Explanation:

The given diameter of the pizza, AE = 20 in.

The measure of the arc AB,
`m\widehat{AB}` = ∠ACB = 65°

The measure of the arc DE,
`m\widehat{DE}` = ∠DCE = 110°

Given that AE is the diameter of the circular pizza, we have;

`m\widehat{BE}` = ∠BCE = 180° - ∠ACB = 180° - 65° = 115°

Similarly;

∠ACD = 180° - ∠DCE = 180° - 110° = 70°

a) The biggest piece of pizza is the piece with the largest angle which is the piece formed by arc BE,
`m\widehat{BE}` = 115°

The piece of pizza she should choose is the piece, BE

b) Arc length = (Arc angle)/360 × (Circumference of the circle)

The circumference of the circular pizza, C = π × Diameter = π × length
`\overline {AE}`

∴ C = π × 20 in.

The arc length of the arc BE = 115/360 × π × 20 = 115·π/18 ≈ 20.07

The length of the cheese in her piece of the crust, l = The arc length of the arc BE ≈ 20.07 inches.