From a rectangular sheet of acrylic of dimensions 32 cm by 24 cm 64 circular buttons, each of diameter 3.5 cm , have been cut out. Find the area of the remaining sheet.
The answer is 152 cm sq
152cmsquare
From a rectangular sheet of acrylic of dimensions 32 cm by 24 cm 64 circular buttons, each of diameter 3.5 cm , have been cut out. Find the area of the remaining sheet.
To find the area of the remaining sheet, we need to subtract the total area of the circular buttons from the area of the original rectangular sheet.
Step 1: Calculate the area of one circular button.
- The diameter of each circular button is 3.5 cm, so the radius (r) is half the diameter, which is 1.75 cm.
- The formula to calculate the area of a circle is A = π * r^2, where π is approximately 3.14.
- Plugging in the values, the area of one circular button is A = 3.14 * (1.75 cm)^2.
Step 2: Calculate the total area of all the circular buttons.
- Since you have mentioned that there are 64 circular buttons, we need to multiply the area of one circular button by 64 to get the total area of all the buttons.
Step 3: Calculate the area of the original rectangular sheet.
- The dimensions of the rectangular sheet are given as 32 cm by 24 cm.
- The formula to calculate the area of a rectangle is A = length * width.
- Plugging in the values, the area of the original rectangular sheet is A = 32 cm * 24 cm.
Step 4: Calculate the area of the remaining sheet.
- To find the area of the remaining sheet, we need to subtract the total area of the circular buttons from the area of the original rectangular sheet.
Let's calculate the values now:
Step 1: The area of one circular button: A = 3.14 * (1.75 cm)^2.
Step 1: A = 3.14 * (3.0625 cm^2).
Step 1: A ≈ 9.6194 cm^2.
Step 2: The total area of all the circular buttons: 64 * 9.6194 cm^2.
Step 3: The area of the original rectangular sheet: A = 32 cm * 24 cm.
Step 3: A = 768 cm^2.
Step 4: The area of the remaining sheet: The area of the original rectangular sheet - the total area of all the circular buttons.
Now, let's substitute the values and calculate the area of the remaining sheet:
Step 4: The area of the remaining sheet: 768 cm^2 - (64 * 9.6194 cm^2).
Calculating this expression will give us the area of the remaining sheet.
sheet area: 32*24
buttons area: 64 * π * 3.5^2
now just subtract