Question

Tylor bought a wedge he measured the arc length of the wedge to be 12 centimeters and the radius to be 8 centimeters. Priya bought a wedge that came from a circular cheese block with a radius of 9 centimeters. The block was cut into 6 congruent sectors which wedge is large? I need be help solving this review question!

Answer 1

Answer

Tylor's wedge is larger

Step-by-step explanation

The interior angle of the whole circular cheese block measures 360°. Given that the block was cut into 6 congruent sectors, then the interior angle of each sector measures:

$\theta=\frac{360\degree}{6}=60\degree$

Arc length formula

$\text{ Arc length }=2\pi r\frac{\theta}{360\degree}$

where r is the radius and θ is the interior angle of the sector.

The cheese block has a radius of 9 cm. Substituting r = 9 cm and θ = 60° into the formula, the arc length of the cheese wedge is:

$\begin{gathered} \text{ Arc length }=2\pi\cdot9\cdot\frac{60}{360} \\ \text{Arc length}\approx9.42\text{ cm} \end{gathered}$

The arc length of Tylor's wedge is 12 cm, then it is larger than Priya's wedge