Answer :
Answer:
The possible values of the width of ledge w are 2 in, 4 in, 6 in, 8 in, 10 in, 12 in, 14 in, 16 in, 18 in, 20 in, 22 in.
Step-by-step explanation:
Since the area of he pit and width of ledge are in a circular pattern, the area of the pit + ledge is given by
A = π(R² - r²) where R = distance from center of pit to outer part of ledge and r = radius of pit.
Since diameter of pit = 16 in, radius of pit, r = 16 in/2 = 8 in.
Also, the maximum area of the pit and ledge is 2826 in². So, A = 2826 in²
Since A = π(R² - r²)
R = √(A/π + r²)
substituting th values of A and r into R, we have
R = √(2826 in²/π + (8 in)²)
R = √(899.54 in² + 64 in²)
R = √963.54 in²
R = 31.04 in
R ≅ 31 in
Now, the maximum width of the ledge w = R - r = 31 - 8 = 23 in.
Since the width of each brick is 2 in, the width of the ledge must be in multiples of 2. Since the maximum width of the ledge is 23 in, we divide it by 2 in to know how many bricks are required for the width of the ledge.
So, number of bricks = 23 in/2 in = 11.5 ≅ 12
So, we require from 1 to 12 bricks to have a minimum to maximum width of ledge.
Since the width of ledge = no of bricks × width of brick
So, the possible values of w are 1 × 2 in, 2 × 2 in, 3 × 2 in, 4 × 2 in, 5 × 2 in, 6 × 2 in, 7 × 2 in, 8 × 2 in, 9 × 2 in, 10 × 2 in, 11 × 2 in
So, the possible values of the width of ledge w are 2 in, 4 in, 6 in, 8 in, 10 in, 12 in, 14 in, 16 in, 18 in, 20 in, 22 in.
We do not include 24 in since the maximum width of the ledge is 23 in.