Answer:
k = 110
Step-by-step explanation:
You want the integer multiple of pi that is the area of 300° of a donut with inner radius 8 cm and outer radius of 14 cm.
Area of a circle
The area of a circle is given by the formula ...
A = πr²
Then the area of the outer circle is ...
A = π(14 cm)² = 196π cm²
The area of the inner circle is ...
A = π(8 cm)² = 64π cm²
Donut area
The area of the whole donut is the difference of these areas:
whole donut area = (196 -64)π cm² = 132π cm²
Shaded area
The shaded area of the figure represents 300° of the 360° full donut. The area is proportional to the central angle, so the shaded area is ...
shaded area = (300°/360°)×whole donut area
shaded area = 5/6 × 132π cm² = 110π cm²
Comparing this to the expression kπ cm², we see that ...
k = 110
