Lesson 16

Applying Area of Circles

Let’s find the areas of shapes made up of circles.

Problem 1

A circle with a 12-inch diameter is folded in half and then folded in half again. What is the area of the resulting shape?

Problem 2

Find the area of the shaded region. Express your answer in terms of \(\pi\).

A shaded rectangle with three unshaded circles stacked one above the other inside the rectangle.

 

Problem 3

The face of a clock has a circumference of 63 in. What is the area of the face of the clock?

(From Unit 5, Lesson 15.)

Problem 4

Which of these pairs of quantities are proportional to each other? For the quantities that are proportional, what is the constant of proportionality?

  1. Radius and diameter of a circle
  2. Radius and circumference of a circle
  3. Radius and area of a circle
  4. Diameter and circumference of a circle
  5. Diameter and area of a circle
(From Unit 5, Lesson 15.)

Problem 5

Find the area of this shape in two different ways.

An odd 6-sided shape with some sides labeled. Starting at the top and moving clockwise, 1 m, 4 m, 3 m, unknown, unknown, 2 m.
(From Unit 5, Lesson 14.)

Problem 6

Elena and Jada both read at a constant rate, but Elena reads more slowly. For every 4 pages that Elena can read, Jada can read 5.

  1. Complete the table.
    pages read by Elena pages read by Jada
    4 5
    1
    9
    \(e\)
    15
    \(j\)
  2. Here is an equation for the table: \(j = 1.25e\). What does the 1.25 mean?
  3. Write an equation for this relationship that starts \(e = \text{...}\)
(From Unit 5, Lesson 2.)