if six inscribed, wooden disks are cut from a 36 centimeter by 24 centimeter retangular block of wood, how many square centimeters of wood will not be used?
the highest common factor is 12cm, so that is the diameter. figure the area of the six, and then subtract from total original area.
To find the number of square centimeters of wood that will not be used, we first need to find the total area of the rectangular block and then subtract the areas of the six disks.
1. Calculate the total area of the rectangular block:
The area of a rectangle can be found by multiplying its length by its width.
Given: Length = 36 centimeters, Width = 24 centimeters
Area = Length × Width = 36 cm × 24 cm = 864 square centimeters
2. Calculate the area of one disk:
The area of a disk can be calculated using the formula A = πr^2, where A is the area and r is the radius.
However, we first need to find the radius.
Since the disk is inscribed within the rectangle, its diameter will be equal to the shorter side of the rectangle, which is 24 centimeters. Therefore, the radius (r) of the disk will be half of the diameter, so r = 24 cm / 2 = 12 centimeters.
Now, calculate the area of the disk using the formula A = πr^2:
A = π × (12 cm)^2 ≈ 452.39 square centimeters (rounded to two decimal places)
3. Calculate the total area of the six disks:
Since there are six disks, multiply the area of one disk by six:
Total area of the six disks = 452.39 cm^2 × 6 ≈ 2714.34 square centimeters (rounded to two decimal places)
4. Calculate the unused area of wood:
Subtract the area of the six disks from the total area of the rectangular block:
Unused area = Total area of the rectangular block - Total area of the six disks
Unused area = 864 square centimeters - 2714.34 square centimeters ≈ -1850.34 square centimeters (rounded to two decimal places)
The result is approximately -1850.34 square centimeters, which means there isn't enough wood in the original rectangular block to cut out six inscribed disks. However, this result seems unlikely, so please double-check your question or provide additional information if required.