NAME:
UNIT 3 • CIRCLES AND VOLUME
Lesson 5: Explaining and Applying Area and Volume Formulas
Practice 3.5.1: Circumference and Area of a Circle
Use your knowledge of circumference and area to complete each problem.
1. A
circle has a regular octagon inscribed in it. The circle has a radius of 4 meters. Find the
perimeter of the octagon. Use the formula 2p r to find the circumference of the circle. Why is the
circumference found by using the formula a different length than the perimeter of the octagon?
2. A
circle has a regular dodecagon (12-sided polygon) inscribed in it. The circle has a radius of
4 meters. Find the perimeter of the dodecagon. Then, find the circumference of the circle using
2p r. Why is the circumference found by using the formula a different length than the perimeter
of the dodecagon?
3. C
ompare the results of problems 1 and 2. Which dissection is a better approximation of the
circumference of the circle? Use a 15-sided regular polygon as the inscribed figure in a circle
that has a radius of 4 meters. Calculate the polygon’s perimeter and compare it with the circle’s
circumference.
4. A
circle has a regular octagon inscribed in it. The circle has a radius of 4 meters. Find the area
of the circle using the formula A = p r 2, then find the area of the octagon. Why is the area of the
circle different from the area of the octagon?
5. A
circle has a regular dodecagon inscribed in it. The circle has a radius of 4 meters. Find the
area of the circle and then of the dodecagon. Why is the area of the circle different from the area
of the dodecagon?
continued
U3-220
CCGPS Analytic Geometry Teacher Resource
© Walch Education
NAME:
UNIT 3 • CIRCLES AND VOLUME
Lesson 5: Explaining and Applying Area and Volume Formulas
6. C
ompare the results of problems 4 and 5. Which dissection is a better approximation of the
area of the circle? Use a 36-sided regular polygon as the inscribed figure in a circle that has a
radius of 4 meters. Calculate the polygon’s area and compare it with the circle’s area.
7. A
round dining room table has a wood top with a circumference of 32 feet. A woodworker is
refinishing the top. He needs to find the area of the top to buy materials and know how long the
job will take. What is the area of the tabletop?
8. A pizza has a circumference of 40 inches. What is the area of the pizza?
9. A
carpenter is installing curved wood trim around a circular window. The window is a circle
that has an area of 50 square feet. How many feet of wood trim are needed to surround the
window? Measure the trim based on the length of the wood next to the window.
10. A
n artist paints a large blue circle on a yellow wall. The area of the painted circle is 150 square
feet. What is the circumference of the circle?
U3-221
© Walch Education
CCGPS Analytic Geometry Teacher Resource