124k views
1 vote
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.

User Edwing
by
7.8k points

1 Answer

0 votes

Answer:

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

Explanation:

Part A) we know that

The scale factor is equal to m

The surface area of the prism is equal to


S=2B+Ph

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


B=xy\ units^(2)


P=2(x+y)\ units


h=z\ units

substitute


SA=[2(xy)+2(x+y)z]\ units^(2)

Prism B


B=(mx)(my)=(xy)m^(2)\ units^(2)


P=2(mx+my)=2m(x+y)\ units


h=mz\ units

substitute


SB=[2(xym^(2))+2m(x+y)mz]\ units^(2)


SB=[2(xym^(2))+2m^(2)(x+y)z]\ units^(2)


SB=m^(2)[2(xy)+2(x+y)z]\ units^(2)

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


V=Bh

where

B is the area of the base

h is the height of the prism

we have

Prism A


B=xy\ units^(2)


h=z\ units

substitute


VA=[(xyz]\ units^(3)

Prism B


B=(mx)(my)=(xy)m^(2)\ units^(2)


h=mz\ units

substitute


VB=[(xym^(2))mz]\ units^(3)


VB=[(xyzm^(3))]\ units^(3)

therefore

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

User Grufas
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories