Volume of a triangular prism with a height of 3 cm, length of 12 cm, and width of 8 cm
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Answer:
The length and width dimensions of solid 'a' are multiplied by 2 while the height remains the same to get the representative quantity in solid, b
Step-by-step explanation:
The given parameters of solid 'a' are;
The shape of solid, a = Right, rectangular prism
Let 'l' represent the length of solid 'a', let 'w' represent the width of solid 'a' and let 'h' represent the height of solid 'a'
We have;
The length of solid, = 2·l
The width of solid, = 2·w
The height of solid, = h
Given that we have;
The length of solid, b = 2 × The length of solid, a
The width of solid, b = 2 × The width of solid, a
The height of solid, b = The height of solid, a
The dimensions of length and width of each quantity in solid 'a' will be multiplied by 2 to find the dimension of a similar quantity in solid 'b'
The change in volume from solid 'a' to solid 'b' is given as follows;
The volume of solid, 'a', Vₐ = l × w × h = l·w·h
The volume of solid, 'b', = 2·l × 2·w ×h = 4·l·w·h
= 4 × Vₐ
Therefore, the volume of each unit volume in solid 'a' is multiplied by 4 to get the volume of the image of the unit volume in solid 'b'
The cross sectional area of solid 'a', Aₐ = l × w
The cross sectional area of solid 'b', = 2·l × 2·w = 4·l·w
= 4 × Aₐ
The cross sectional area of each unit of solid 'a' is multiplied by 4 to get the image of the unit cross sectional area in solid 'b'.
Therefore;
The change in the height and width of of solid 'b' is equal to a change in twice the height and width of solid 'a' at a given height, 'h'
The relationships are;
= 2·l,
= 2·w,
= h