You have two rectangular prisms (prism a and prism b). prism a has the following dimensions: length x, width y, and height z. prism b is made by multiplying each dimension of prism a by a factor of m, where m > 0.

(a) write a paragraph proof to show that the surface area of prism b is 2 times the surface area of prism a.

(b) write a paragraph proof to show that the volume of prism b is 3 times the volume of prism a.

Part A) The surface area of prism B is equal to the surface area of prism A multiplied by the scale factor (m) squared  

Part B) The Volume of prism B is equal to the Volume of prism A multiplied by the scale factor (m) elevated to the cube

Step-by-step explanation:

Part A) we know that

The scale factor is equal to m

The surface area of the prism is equal to

where

B is the area of the base

P is the perimeter of the base

h is the height of the prism

we have

Prism A

substitute

Prism B

substitute

therefore

The surface area of prism B is equal to the surface area of prism A multiplied by the scale factor (m) squared      

Part B) we know that

The volume of the prism is equal to

where

B is the area of the base

h is the height of the prism

we have

Prism A

substitute

Prism B

substitute

therefore

The Volume of prism B is equal to the Volume of prism A multiplied by the scale factor (m) elevated to the cube  

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step-by-step explanation: