From a rectangular metal sheet 35cm × 42 cm, a circular sheet as big as possible is cut off. Find the area of the remaining sheet.
Answers
Area of the rectangle is = l x b
= 35 x 42 = 1470cm^2
The area of the remaining metal sheet is 507.5 cm².
• Given dimensions of the rectangular sheet are : 35 cm × 42 cm
∴ Area of the rectangular sheet = 35 cm × 42 cm = 1470 cm²
• The largest possible circle can be cut off touching the longer sides of the sheet, i.e., 42 cm.
• If the circle is cut off touching all sides of the sheet, then the shape will be oval and not circular (Refer to the image attached below).
• Therefore, the circle will have the diameter of the shorter side, i.e., 35 cm.
Now, Radius of the circle (r) = Diameter / 2 = 35 cm / 2
• Area of the circle cut out = π.r²
= (22 / 7) × (35 cm / 2)²
= (22 / 7) × (35 cm / 2) × (35 cm / 2)
= (22 × 35 cm × 35 cm) / (7 × 2 × 2)
= (11 × 5 × 35) cm² / 2
= 1925 cm² / 2
= 962.5 cm²
• Area of the sheet left = Total area of the sheet - Area of the circle cut out
=> Area of the sheet left = 1470 cm² - 962.5 cm² = 507.5 cm²
