What cross-sections do you get when you give a vertical cut horizontal cut to the following solids/figure?
Solids/figure horizontal cut vertical cut A ball A duster A birthday cap A cylinder
| Solids/figure | horizontal cut | vertical cut |
| A ball | ||
| A duster | ||
| A birthday cap | ||
| A cylinder |
Answer
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Hint: To solve this question, we will have to analyze all the different given objects separately. Then we have to figure out the cross-sections by the horizontal and vertical cuts. Then we need to analyze the shape generated by the cross-sections. Once the figures are cut horizontally or vertically they will generate a \[2\] - dimensional cross-section surface.
Complete answer:
A ball:
A ball is spherical. If we cut it horizontally and vertically the cross-sections generated by them will be a two-dimensional figure. Both the cuts will generate a circular cross-section.
A duster:
A duster is mostly like a cuboid. If we cut it horizontally and vertically the cross-sections generated by them will be a two-dimensional figure. Both the cuts will generate a rectangular cross-section.
A birthday cap:
A birthday cup is like a cone. If we cut it horizontally and vertically the cross-sections generated by them will be a two-dimensional figure. The horizontal cut will generate a circular cross-section while the vertical cut will give a triangular cross-section.
A cylinder:
If we cut it horizontally and vertically the cross-sections generated by them will be a two-dimensional figure. The horizontal cut will generate a circular cross-section while the vertical cut will give a rectangular cross-section.
$\therefore $ The table will look like this:
Note:
We should be well equipped with the shapes of the solids. Based on the shape of the objects, the horizontal and vertical cuts will determine the cross-sections of different objects. We should also be well acquainted with two-dimensional figures. Many objects of different shapes may have the same cross-section surface.
Complete answer:
A ball:
A ball is spherical. If we cut it horizontally and vertically the cross-sections generated by them will be a two-dimensional figure. Both the cuts will generate a circular cross-section.
A duster:
A duster is mostly like a cuboid. If we cut it horizontally and vertically the cross-sections generated by them will be a two-dimensional figure. Both the cuts will generate a rectangular cross-section.
A birthday cap:
A birthday cup is like a cone. If we cut it horizontally and vertically the cross-sections generated by them will be a two-dimensional figure. The horizontal cut will generate a circular cross-section while the vertical cut will give a triangular cross-section.
A cylinder:
If we cut it horizontally and vertically the cross-sections generated by them will be a two-dimensional figure. The horizontal cut will generate a circular cross-section while the vertical cut will give a rectangular cross-section.
$\therefore $ The table will look like this:
| Solids/figure | horizontal cut | vertical cut |
| A ball | circle | circle |
| A duster | rectangle | rectangle |
| A birthday cap | circle | triangle |
| A cylinder | circle | rectangle |
Note:
We should be well equipped with the shapes of the solids. Based on the shape of the objects, the horizontal and vertical cuts will determine the cross-sections of different objects. We should also be well acquainted with two-dimensional figures. Many objects of different shapes may have the same cross-section surface.
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