Respuesta :
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, [tex]l_b[/tex] = 2·l
The width of solid, [tex]w_b[/tex] = 2·w
The height of solid, [tex]h_b[/tex] = 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', [tex]V_b[/tex] = 2·l × 2·w ×h = 4·l·w·h
[tex]V_b[/tex] = 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', [tex]A_b[/tex] = 2·l × 2·w = 4·l·w
[tex]A_b[/tex] = 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;
[tex]l_b[/tex] = 2·l, [tex]w_b[/tex] = 2·w, [tex]h_b[/tex] = h
