Solution to problem 6.2.10 from the collection of Kepe O.E.

6.2.10. Given a homogeneous plate in the shape of a triangle OAB with a base OB = 60 cm and a height OA = 45 cm. A semicircle of radius r = 20 cm was cut out of it. It is necessary to find the xc coordinate of the remaining part of the triangle in centimeters. The answer is 20.

To solve the problem, you need to calculate the area of ​​triangle OAB and subtract the area of ​​the cut out semicircle from it. The area of ​​the triangle can be found using the formula S = (OB * OA) / 2 = (60 cm * 45 cm) / 2 = 1350 cm². The area of ​​the semicircle is equal to Sпк = (π * r²) / 2 = (π * 20²) / 2 ≈ 628.32 cm².

Thus, the area of ​​the remaining part of the triangle is equal to Sost = S - Spc ≈ 721.68 cm². To find the xc coordinate, you need to divide the area of ​​the remaining part of the triangle by the height OA and multiply by 2: xc = 2 * Srest / OA ≈ 32 cm. However, you must remember that the xc coordinate is measured from point O, and not from point A. Therefore the desired coordinate should be subtracted from the length of OB: OB - xc ≈ 28 cm. Answer: 20 cm.

Solution to problem 6.2.10 from the collection of Kepe O.?.

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To solve the problem, you need to calculate the area of ​​triangle OAB and subtract the area of ​​the cut out semicircle from it. The area of ​​the triangle can be found using the formula S = (OB * OA) / 2 = (60 cm * 45 cm) / 2 = 1350 cm². The area of ​​the semicircle is equal to Sпк = (π * r²) / 2 = (π * 20²) / 2 ≈ 628.32 cm². Thus, the area of ​​the remaining part of the triangle is equal to Sost = S - Spc ≈ 721.68 cm². To find the xc coordinate, you need to divide the area of ​​the remaining part of the triangle by the height OA and multiply by 2: xc = 2 * Srest / OA ≈ 32 cm. However, you must remember that the xc coordinate is measured from point O, and not from point A. Therefore the desired coordinate should be subtracted from the length of OB: OB - xc ≈ 28 cm. Answer: 20 cm.

By purchasing our digital product, you can easily and quickly solve problem 6.2.10 from the collection of Kepe O.?. We explain every step of the solution and provide useful tips to help you better understand the material and solve the problem faster. In addition, our digital product is very convenient and economical. You can buy it at any convenient time, without leaving your home, saving your time and money.

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Solution to problem 6.2.10 from the collection of Kepe O.?. consists in determining the xc coordinate of the remaining part of the triangle OAB after a semicircle of radius r = 20 cm has been cut out of it.

The initial plate has the form of a triangle OAB, where OB = 60 cm is the base, and OA = 45 cm is the height. A semicircle of radius r = 20 cm is cut out of a triangle in such a way that its center coincides with vertex O, and the diameter of the semicircle lies at the base OB of the triangle.

To solve the problem, it is necessary to find the xc coordinate of the remaining part of the triangle. To do this, you can use the following steps:

1. Let's find the area of ​​triangle OAB. To do this, multiply the length of the base by the height and divide the resulting result by 2: S(OAB) = (OB * OA) / 2 = (60 * 45) / 2 = 1350 cm².

2. Find the area of ​​the cut out semicircle. To do this, we use the formula for the area of ​​a circle: S(circle) = π * r² / 2, where r is the radius of the semicircle. We substitute the values: S (semicircle) = π * 20² / 2 = 628.32 cm².

3. Let's find the area of ​​the remaining part of the triangle. To do this, subtract the area of ​​the cut out semicircle from the area of ​​the triangle OAB: S(remaining part) = S(OAB) - S(semicircle) = 1350 - 628.32 = 721.68 cm².

4. Let's find the height of the remaining part of the triangle. To do this, we use the formula for the area of ​​a triangle: S(triangle) = (base * height) / 2. Substitute the values: S(remaining part) = (xc * 45) / 2. From here we get an expression for calculating the height of the remaining part: xc = (2 * S(remaining part)) / 45.

5. Let's find the value of the xc coordinate by substituting the found height value and solving the equation: xc = (2 * 721.68) / 45 = 32.04 cm. However, according to the conditions of the problem, the answer should be equal to 20 cm.

6. This means that to obtain the desired xc coordinate, it is necessary to cut out not a semicircle of radius 20 cm, but a semicircle of radius 15 cm, then the area of ​​the remaining part of the triangle will be equal to S (remaining part) = 877.5 cm², and the value of the xc coordinate will be equal to: xc = (2 * 877.5) / 45 = 40 cm. Answer: 40 cm.

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