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What cross-sections do you get when you give a
$(i)$ vertical cut
$(ii)$ horizontal cut to the following solids?
$(a)$ A brick
$(b)$ A round apple
$(c)$ A die
$(d)$ A circular pipe
$(e)$ An ice cream cone
Given: Different solids: $(a)$ A brick $(b)$ A round apple $(c)$ A die
$(d)$ A circular pipe $(e)$ An ice cream cone.
To do: To find the cross-section obtained when: $(i)$ vertical cut $(ii)$ horizontal cut is given to the solids.
Solution:
We know that if we give a cut ($vertical\ and\ horizontal)$ to a solid shape then we obtain different type of cross sections in different solids:
Shapes | Vertical Cut | Horizontal Cut |
Cube | 2 rectangular face shapes | 2 rectangular face shapes |
Cuboid | 2 rectangular face shapes | 2 rectangular face shapes |
Cylinder | 2 rectangular face shapes | 2 cylindrical shapes |
Sphere | 2 semi-circular face shapes | 2 semi-circular face shapes |
Cone | 2 triangular face shapes | 1 small cone and 1 frustum |
$(a)$ A brick
Vertical cut: We will get 2 rectangle shape pieces of length half the length of brick but the breath will be the same
Horizontal cut: We will get 2 pieces of rectangle shape each of the same lengths but with half the breadth of the brick.
$(b)$ A round apple
Vertical cut: We will get 2 semi-circle shape pieces of the same diameter.
Horizontal cut: We will get 2 semi-circle shape pieces of the same diameter.
$(c)$ A dice
Vertical cut: We will get 2 rectangular shape pieces of length half the side of the dice but the breath will be the same as the side of the dice.
Horizontal cut: We will get 2 pieces of rectangular shape each of length equal to the side of dice but breadth will be half of the side of dice.
$(d)$ A circular pipe
Vertical cut: We will get 2 rectangular shape pieces. Length will be equal to the height of the circular pipe and breadth will be equal to the diameter of the circular pipe
Horizontal cut: We will get 2 pieces of circular pipe but their height will be half of the original circular pipe
$(e)$ An ice cream cone
Vertical cut: We will get 2 triangular shape pieces
Horizontal cut: We will get 1 piece of small cone shape and 1 frustum shape piece.
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