The height of the cylinder is 16cm, the radius of its base is 10cm. Find the cross-sectional area of the cylinder by a plane parallel to its axis, taking into account that the distance between this plane and the axis is 6 cm.
The plane of the section is a parallelogram, where one side is equal to the height of the cylinder, the area of this section is sought after the formula S = H * a, where a is unknown.
To find it, we draw from the base of the height O of the cylinder the height of OM to the side a of the section, where this height, by condition, is 6 cm, and it will divide the side a into two.
Let’s draw a segment OP connecting the base of the height O and the point of contact of side a with the base of the cylinder, this will be the radius.
Then from the right-angled triangle OMР we find the segment OM behind the Pythagorean theorem, it is equal to: √ (100 – 36), this is 8 cm.
Then the entire side will be 8 * 2 = 16 cm.
Knowing all the necessary values, we find the cross-sectional area: 16 * 16 = 256 cm2.
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