Geometry Rotating book | Mathematics | Page 1

edgy canyon Dec 1, 2023, 9:20 PM

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i need help with a geometry task it says: Imagine your math book is a rectangle. This rectangle stands on a corner and is held by the opposite corner. Your book rotates around the imaginary line (s. Fig.), which encloses a right angle with the table.

A) Draw an exact oblique image on white paper on a scale of 1:2. Enter all values and guidelines that have been measured or calculated (with a solution).

B) Calculate the volume and surface content of the resulting body.

For A I kind of know what to do but i’m stuck on B. The Book is 20x26,5cm and the rotation axis is 33.2cm. Now i don’t know how i’m supposed to calculate the volume and surface content 🥹

visual rapidsBOT Dec 1, 2023, 9:20 PM

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Geometry Rotating book

marble matrix Dec 2, 2023, 4:14 PM

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Well, here's the shape that is created by the math book which is being rotated around an axis.

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You can easily see that the shape is actually composed of four cones, each with the measurement that can be calculated.

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Note that the blue-coloured rectangle represents the book when it is not spun, the pink-coloured one is when the book is at the opposite side of the original spot.

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You can easily see the cross section through the imaginary axis is a weird-looking, but manageable kind of shape.

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edgy canyon Dec 3, 2023, 8:22 AM

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alright so should i calculate the two cones and then the two cone part things? And then add it all up

edgy canyon Dec 3, 2023, 11:00 AM

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does this make sennse?

#Geometry Rotating book