Question

22) The base of a lampshade is circular. The circumference of the base is 3 times the radius increased by 4.25 inches.

Find the radius of the circular base. Round your answer to the nearest tenth.

Answer 1

To find the radius of the circular base of the lampshade, set up an equation using the given information and solve for 'r' by isolating it.

Step-by-step explanation:

To find the radius of the circular base of the lampshade, we can set up an equation using the given information. Let's denote the radius as 'r'. The circumference of the base is 3 times the radius increased by 4.25 inches, so we have the equation 2πr = 3r + 4.25. To solve for 'r', we can rearrange the equation as 2πr - 3r = 4.25, then combine the 'r' terms to get (2π - 3)r = 4.25. Finally, we divide both sides of the equation by (2π - 3) to isolate 'r' and find the value of the radius.

Answer 2

~1.29 inches

Step-by-step explanation:

C = 2πr

C = 3r + 4.25

2πr = 3r + 4.25

2πr - 3r = 4.25

r(2π-3) = 4.25

r = 4.25/(2π-3) ≈ 1.29