Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Solutions to various geometry problems involving finding the circumference and area of circles, as well as the area of shaded regions. The problems are presented in terms of different units, including inches, centimeters, and feet. The solutions are given in terms of π and the appropriate units.
Typology: Lecture notes
1 / 12
This page cannot be seen from the preview
Don't miss anything!
Section 2.2 Solutions
Homework #1-4: Find the circumference of each circle. Make sure to include the proper units in your answer. Leave your answer in terms of 𝜋.
𝐶 = 2 𝜋𝑟
C = 2 𝜋( 14 𝑚)
Answer: 28 𝜋 m
C = 𝜋𝑑
Answer: 16 𝜋 𝑐𝑚
P = 2(8cm + 4cm) P = 2(12 cm)
Answer: 24 cm
P = 4 cm + 4 cm + 10 cm + 10 cm
P = 28 cm
P = 124 ft + 156 ft + 156 ft
Answer: 436 ft
P = 5 in + 8 in + 3 in + 4 in
Answer: 20 in
Homework: #13 – 24 Find the area of each figure. Use appropriate units.
Area = 225 in^2
A = (10.3 cm)(6.2 cm)
Answer: 63.86 cm^2
Area = (^13.^4 𝑚+^7.^22 𝑚)(^10.^6 𝑚)
Area= 128.26 m^2
Area =
( 20 𝑐𝑚+ 6 𝑐𝑚)( 10 𝑐𝑛) 2
Area = (260 cm^2 )/
Answer: 130 cm^2
Area = (36m^2 )/
Answer: 18 m^2
A = (9cm)(16cm)
Answer: 144 cm^2
Answer: 64 in^2
Answer: 16 𝜋 𝑐𝑚^2
A = 𝜋(3")^2
Answer: 9 𝜋 𝑠𝑞𝑢𝑎𝑟𝑒 𝑖𝑛𝑐ℎ𝑒𝑠
First calculate the area as if the entire shape was shaded.
Area all shaded = 𝜋( 10 𝑓𝑡)^2 = 100 𝜋 𝑓𝑡^2
Next find the area of the unshaded region.
Area unshaded = 𝜋( 5 𝑓𝑡)^2 = 25 𝜋 𝑓𝑡^2
Finally subtract the amounts.
Answer: 100 𝜋 𝑓𝑡^2 − 25 𝜋 𝑓𝑡^2 = 75 𝜋 𝑓𝑡^2
First calculate the area as if the entire shape was shaded.
Area if entire shape was shaded:
This is a circle with radius 5 m.
Area all shaded = 3.14(5m)^2 = 78.5 m^2
Next find the area of the unshaded region.
Area unshaded = (7m)^2 = 49 m^2
Finally subtract the amounts.
Answer: 78.5 m^2 – 49 m^2 = 29.5 m^2
Area all shaded = (15mm)^2 = 225mm^2
Next find the area of the unshaded region.
Area unshaded = (5mm)^2 = 25mm^2
Finally subtract the results
Answer: 225 mm^2 – 25 mm^2 = 200 mm^2
Area all shaded = (30cm)(15cm)= 450 cm^2
Next find the area of the unshaded region.
Area unshaded = (11cm)(22cm) = 242 cm^2
Finally subtract the amounts
Answer: 450 cm^2 – 242 cm^2 = 208 cm^2
