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enter image description here

The shape of the spatial geometry is shown in the above figure. Specifically, it is as follows:

This is a cup with parallel circular surfaces at the top and bottom, and a portion of a spherical surface on the side. The radius of the sphere where the sphere is located is 5cm, with a diameter of 4Sqrt [6] cm at the top and 6cm at the bottom. The distance between the top and bottom surfaces is 3cm.

Calculate the volume of the cup, ignoring the thickness of the cup. And calculate the surface area of the cup, and finally draw the image of the cup.

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  • 1
    $\begingroup$ Homework question? We don't like them here. (I did not downvote, just saying.) $\endgroup$
    – Henrik Schumacher
    Commented Dec 5, 2023 at 0:31
  • 2
    $\begingroup$ Freeform input: = Spherical Frustrum $\endgroup$
    – Syed
    Commented Dec 5, 2023 at 3:06
  • $\begingroup$ @HenrikSchumacher This is the problem I encountered, not just trying to complete the task $\endgroup$
    – csn899
    Commented Dec 5, 2023 at 7:57
  • $\begingroup$ @Syed This feature is very powerful, with images and calculation formulas $\endgroup$
    – csn899
    Commented Dec 5, 2023 at 7:58

1 Answer 1

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The volume and area of a spherical layer are:

vol= Pi/6 h (3 r1^2+3 r2^2+ h^2);

area= Pi (2 r h + r1^2 + r2^2);

Therefore for your example:

vol= Pi/2 (3 (2 Sqrt [6])^2 + 3 3^2 + 3^2)

54 \[Pi]

area= Pi (2 5 3 + (2 Sqrt [6])^2 +  3^2)

63 \[Pi]

To draw the bowl:

Show[RevolutionPlot3D[-Sqrt[5^2 - h^2], {h, 3, 2 Sqrt[6]}],
 Graphics3D[Cylinder[{{0, 0, -4}, {0, 0, -4.01}}, 3]]]

enter image description here

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  • $\begingroup$ Which quantity does r represent in the formula for calculating surface area?area= Pi (2 r h + r1^2 + r2^2); $\endgroup$
    – csn899
    Commented Dec 5, 2023 at 11:07
  • $\begingroup$ rDoes it represent the radius of the spherical sphere on which the side is located? $\endgroup$
    – csn899
    Commented Dec 5, 2023 at 11:10
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    $\begingroup$ r1 and r2 are the radius of the openings. r is the spherical radius. $\endgroup$
    – Daniel Huber
    Commented Dec 5, 2023 at 11:21
  • $\begingroup$ [-Sqrt[5^2 - h^2]What does this parameter in the command mean? $\endgroup$
    – csn899
    Commented Dec 5, 2023 at 11:31
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    $\begingroup$ radius at height h (h->z coordinate) $\endgroup$
    – Daniel Huber
    Commented Dec 5, 2023 at 11:34

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