Find the area of the axial section of the cylinder if the diagonal of the axial section is 17 cm

| August 3, 2021 | education

Find the area of the axial section of the cylinder if the diagonal of the axial section is 17 cm and the height is 11 cm greater than the radius.

The axial section of the cylinder is a rectangle ABCD, then the diagonal AC divides the section into two rectangular, equal triangles.

Let the radius of the circle be R cm, then the leg AD = 2 * R cm, leg CD = R + 11 cm.

By the Pythagorean theorem, AD ^ 2 = AC ^ 2 – CD ^ 2.

4 * R ^ 2 = 289 – (R + 11) ^ 2.

4 * R ^ 2 = 289 – R2 – 22 * ​​R – 121.

5 * R ^ 2 + 22 * ​​R – 168 = 0.

Let’s solve the quadratic equation.

D = b ^ 2 – 4 * a * c = 22 ^ 2 – 4 * 5 * (-168) = 484 + 3360 = 3844.

R1 = (-22 – √3844) / (2 * 5) = (-22 – 62) 10 = -84 / 10 = -8.4. (does not match, since <0).

R2 = (-22 + √3844) / (2 * 5) = (-22 + 62) / 10 = 40/10 = 4.

Then AD = 2 * 4 = 8 cm, CD = 4 + 11 = 15 cm.

Then the cross-sectional area is equal to: Ssection = AD * CD = 8 * 15 = 120 cm2.

Answer: The cross-sectional area is 120 cm2.



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