Math Problem Statement

The circumference of the given circle in terms of p is ___ p in. (Given: radius of the circle = 16.5 inches)

Solution

The image shows a circle with a radius of 16.5 inches, and the question asks to find the circumference of the circle in terms of pp.

The formula for the circumference CC of a circle is given by:

C=2πrC = 2 \pi r

Where rr is the radius of the circle. In this case, r=16.5r = 16.5 inches, so the circumference in terms of π\pi would be:

C=2π×16.5=33πC = 2 \pi \times 16.5 = 33 \pi

Therefore, the circumference of the circle is 33π33 \pi inches.

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:

  1. What is the area of the circle with radius 16.5 inches in terms of π\pi?
  2. How would the circumference change if the radius were doubled?
  3. Can you explain how the formula for circumference is derived from the properties of a circle?
  4. How does the circumference change if you change the radius by a factor of kk?
  5. What is the difference between the circumference and the diameter of a circle?

Tip: The circumference formula uses 2πr2 \pi r, while the area formula uses πr2\pi r^2. Both involve the radius and π\pi, but the operations differ: circumference involves multiplication, and area involves squaring.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circle
Circumference

Formulas

Circumference of a circle: C = 2πr

Theorems

Properties of a circle
Circumference theorem

Suitable Grade Level

Grades 8-10