#5) 7.065 sq. ft. #6) 36 ft #7) 200.96 sq. ft. #8) 176.625 sq. ft.
Explanation #5) Converting 18 inches to feet, 18/12 = 1.5. The area of the circle would be given by A=3.14(1.5)² = 3.14(2.25) = 7.065 sq. ft.
#6) The radius is 18 inches, so the diameter is twice that: 18*2 = 36 inches. Converting this to feet, we have 36/12 = 3 feet. Each stone is 3 feet across. Laying 12 of them against each other would give us a total length of 12*3 = 36 feet.
#7) The radius of the entire mirror with frame is 20/2 = 10. The area of the entire mirror with frame is A=3.14(10²) = 3.14(100) = 314 in². The area of the mirror without the frame is A=3.14(6²) = 3.14(36) = 113.04 in².
The difference between the two will give the area of the frame: 314-113.04 = 200.96 in²
#8) The area of the circular region is given by A=3.14(7.5²) = 176.625 ft²
For this case we have the following diagonals: AE = 40 ST = x + 5 The intersection of the diagonals occurs when: AE = ST Therefore, matching we have: 40 = x + 5 Clearing x we have: x = 40-5 x = 35 Answer: The value of x is: x = 35
