Respuesta :
Answer:
Part A) The scale factor is [tex]2[/tex]
The dimensions of the larger rectangular prism are
[tex]Length=16\ ft[/tex]
[tex]Width=4\ ft[/tex]
[tex]Heigth=12\ ft[/tex]
Part B) The volume of the smaller rectangular prism is [tex]96\ ft^{3}[/tex]
Part C) The volume of the enlarged rectangular prism is [tex]768\ ft^{3}[/tex]
Step-by-step explanation:
Part A)
we know that
If the dimensions of the prism are doubled, then the scale factor is equal to [tex]2[/tex]
so
To find the dimensions of the larger rectangular prism, multiply the scale factor by the dimensions of the smaller rectangular prism
[tex]Length=2*8=16\ ft[/tex]
[tex]Width=2*2=4\ ft[/tex]
[tex]Heigth=2*6=12\ ft[/tex]
Part B) What is the volume of the smaller rectangular prism?
we know that
The volume of a rectangular prism is equal to
[tex]V=LWH[/tex]
we have
[tex]L=8\ ft[/tex]
[tex]W=2\ ft[/tex]
[tex]H=6\ ft[/tex]
substitute the values
[tex]V=8*2*6=96\ ft^{3}[/tex]
Part C) What is the volume of the enlarged rectangular prism?
we know that
The volume of a rectangular prism is equal to
[tex]V=LWH[/tex]
we have
[tex]L=16\ ft[/tex]
[tex]W=4\ ft[/tex]
[tex]H=12\ ft[/tex]
substitute the values
[tex]V=16*4*12=768\ ft^{3}[/tex]
Remember that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
z------> scale factor
x-----> volume of the enlarged prism
y-----> volume of the smaller prism
so
[tex]z^{3}=\frac{x}{y}[/tex]
[tex]x=y*z^{3}[/tex]
we have
[tex]z=2[/tex]
[tex]y=96\ ft^{3}[/tex]
substitute
[tex]x=96*2^{3}=768\ ft^{3}[/tex] ---> is ok
Step-by-step explanation:
Dimensions of the right rectangular prism :
Length of the right rectangular prism = l = 8 ft
Width of the right rectangular prism = b = 2 ft
Height of the right rectangular prism = h = 6 ft
The dimensions of the prism are doubled and dimensions of enlarged prism are:
Length of the larger right rectangular prism = L = 16 ft
Width of the larger right rectangular prism = B = 4 ft
Height of the larger right rectangular prism = H = 12 ft
The scale factor from the smaller rectangular prism to the larger rectangular prism :
Scale factor = [tex]\frac{l}{L}=\frac{b}{B}=\frac{h}{H}[/tex]
Scale factor = [tex]\frac{l}{L}=\frac{8}{16}=0.5[/tex]
0.5 is the scale factor from the smaller rectangular prism to the larger rectangular prism.
The volume of the smaller rectangular prism :
Area of the base of prism = [tex]l\times b[/tex]
V = Area of rectangle × Height :
[tex]V= l\times b\times h = 8 ft\times 2 ft\times 6 ft=96 ft^3[/tex]
The volume of the enlarged rectangular prism :
Area of the base of enlarged prism = [tex]L\times B[/tex]
V' = Area of rectangle × Height :
[tex]V'= L\times B\times H = 8 ft\times 2 ft\times 6 ft=768 ft^3[/tex]
