Question

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Answer 1

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 = $\frac{l}{L}=\frac{b}{B}=\frac{h}{H}$

Scale factor = $\frac{l}{L}=\frac{8}{16}=0.5$

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 = $l\times b$

V = Area of rectangle × Height :

$V= l\times b\times h = 8 ft\times 2 ft\times 6 ft=96 ft^3$

The volume of the enlarged rectangular prism :

Area of the base of enlarged prism = $L\times B$

V' = Area of rectangle × Height :

$V'= L\times B\times H = 8 ft\times 2 ft\times 6 ft=768 ft^3$

Answer 2

Answer:

Part A) The scale factor is $2$

The dimensions of the larger rectangular prism are

$Length=16\ ft$

$Width=4\ ft$

$Heigth=12\ ft$

Part B) The volume of the smaller rectangular prism is $96\ ft^{3}$

Part C) The volume of the enlarged rectangular prism is $768\ ft^{3}$

Step-by-step explanation:

Part A)

we know that

If the dimensions of the prism are doubled, then the scale factor is equal to $2$

so

To find the dimensions of the larger rectangular prism, multiply the scale factor by the dimensions of the smaller rectangular prism

$Length=2*8=16\ ft$

$Width=2*2=4\ ft$

$Heigth=2*6=12\ ft$

Part B) What is the volume of the smaller rectangular prism?

we know that

The volume of a rectangular prism is equal to

$V=LWH$

we have

$L=8\ ft$

$W=2\ ft$

$H=6\ ft$

substitute the values

$V=8*2*6=96\ ft^{3}$

Part C) What is the volume of the enlarged rectangular prism?

we know that

The volume of a rectangular prism is equal to

$V=LWH$

we have

$L=16\ ft$

$W=4\ ft$

$H=12\ ft$

substitute the values

$V=16*4*12=768\ ft^{3}$

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

$z^{3}=\frac{x}{y}$

$x=y*z^{3}$

we have

$z=2$

$y=96\ ft^{3}$

substitute

$x=96*2^{3}=768\ ft^{3}$ ---> is ok