A rectangular piece of metal with 4 equally sized circular holes have a diameter of 12 cm cut from it. Calculate the area of metal after the holes have been cut out
339.12cm squared
Rectangle formula : l x w
Circle : π × r2
L W - 4 (pi D^2/4)
To calculate the area of the metal after the holes have been cut out, you need to find the area of the rectangular piece and then subtract the combined area of the circular holes.
Step 1: Calculate the area of the rectangular piece.
The formula for the area of a rectangle is length times width.
In this case, you have a rectangular piece of metal, but the dimensions are not given. Let's assume the length (l) is 20 cm and the width (w) is 15 cm.
Area of the rectangular piece = length × width
Area = 20 cm × 15 cm = 300 cm²
Step 2: Calculate the combined area of the circular holes.
Given that you have 4 equally sized circular holes with a diameter of 12 cm, you can calculate the area of a single hole and then multiply it by 4.
The formula for the area of a circle is π × radius².
To find the radius (r), divide the diameter by 2.
Radius (r) = 12 cm ÷ 2 = 6 cm
Area of a single hole = π × r²
Area of a single hole = π × 6 cm × 6 cm (using the value of π as approximately 3.14159)
Area of a single hole ≈ 113.097 cm²
Combined area of the circular holes = 4 × area of a single hole
Combined area of the circular holes = 4 × 113.097 cm² = 452.388 cm² (rounded to three decimal places)
Step 3: Calculate the area of the metal after the holes have been cut out.
Subtract the combined area of the circular holes from the area of the rectangular piece.
Area of the metal after holes have been cut out = Area of the rectangular piece - Combined area of the circular holes
Area of the metal after holes have been cut out = 300 cm² - 452.388 cm²
Area of the metal after holes have been cut out ≈ -152.388 cm² (rounded to three decimal places)
Since the result is negative, it seems there might be some error in the calculations or the assumptions made. Please double-check the given values and formulas used for accuracy. The actual area of the metal after the holes have been cut out should be a positive value.