71 309.0 1. A plumber was working on his area when he noticed an open manhole. He wanted to cover it for their safety, so he got an old manhole cover with a base area of 4 500 sq. cm. If the diameter of the open manhole is 75 cm, would the cover fit there?
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Step-by-step explanation:
To determine if the old manhole cover would fit the open manhole, we need to compare their sizes.
The area of a circle can be found using the formula A = πr^2, where r is the radius of the circle and π (pi) is a constant value of approximately 3.14.
Given the diameter of the open manhole is 75 cm, we can find its radius as:
r = d/2 = 75/2 = 37.5 cm
The area of the open manhole can then be calculated as:
A = πr^2 = 3.14 x (37.5)^2 = 4,402.8 sq. cm
Comparing this to the area of the old manhole cover (4,500 sq. cm), we can see that the cover is slightly larger. Therefore, the cover would fit over the open manhole with a diameter of 75 cm.