University:
California State University, Northridge
Course:
MATH 262 | Introduction to Linear Algebra
Academic year:

2024
Views:

368

Pages:

1
Author:

Beckett Gray

Question 1 A circle has a circumference of 48 𝜋 48π centimeters. If the radius of the circle is multiplied by 9, what is the circumference of the new circle? Answer Use the formula for the circumference of a circle: 𝐶 = 2 𝜋 𝑟 C=2πr Let 𝑟 r be the radius of the original circle. Then: 2 𝜋 𝑟 = 48 𝜋 2πr=48π Solve for 𝑟 r: 𝑟 = 48 𝜋 2 𝜋 = 24 cm . r= 2π 48π =24cm. For the new circle, the radius is multiplied by 9: 𝑟 new = 24 × 9 = 216 cm . r new =24×9=216cm. The new circumference is: 𝐶 new = 2 𝜋 𝑟 new = 2 𝜋 ( 216 ) = 432 𝜋 cm . C new =2πr new =2π(216)=432πcm. Note: You can also directly multiply the original circumference 48 𝜋 48π by 9 since the circumference is proportional to the radius: 𝐶 new = 9 × 48 𝜋 = 432 𝜋 cm . C new =9×48π=432πcm. Question 2 What is the area of a circle with a radius of 8 inches? Answer The formula for the area of a circle is: 𝐴 = 𝜋 𝑟 2 A=πr 2 Substitute 𝑟 = 8 inches r=8inches and 𝜋 = 3.14 π=3.14: 𝐴 = ( 3.14 ) ( 8 ) 2 A=(3.14)(8) 2 𝐴 = ( 3.14 ) ( 64 ) A=(3.14)(64) 𝐴 = 200.96 square inches . A=200.96square inches. Question 3 A bicycle tire has a diameter of 27 inches. How far does the bike travel along the ground when the wheel rotates once? Answer When the wheel rotates once, it travels a distance equal to the circumference of the circle. The circumference in terms of the diameter 𝑑 d is: 𝐶 = 𝜋 𝑑 C=πd Substitute 𝑑 = 27 d=27: 𝐶 = 𝜋 ( 27 ) ≈ 3.14 × 27 = 84.8 inches . C=π(27)≈3.14×27=84.8inches. Thus, the bike travels approximately 84.8 inches.