Which shows the dimensions of two rectangular prisms that have volumes of 240 ft3 but different surface areas?A) 8 ft by 5 ft by 6 ft and 5 ft by 6 ft by 8 ftB) 8 ft by 5 ft by 6 ft and 10 ft by 8 ft by 3 ftC) 15 ft by 8 ft by 2 ft and 6 ft by 4 ft by 15 ftD) 12 ft by 6 ft by 5 ft and 8 ft by 10 ft by 3 ft

Calculate the volume and surface areas of both rectangular prisms for each option.

A:

Rectangular Prism #1
[tex]\sf V=lwh[/tex]
[tex]\sf V=(8)(5)(6)=240~ft^3[/tex]

[tex]\sf A=2((8)(5)+(6)(5)+(6)(8))[/tex]
[tex]\sf A=236~ft^2[/tex]

Rectangular Prism #2
[tex]\sf V=lwh[/tex]
[tex]\sf V=(5)(6)(8)=240~ft^3[/tex]

[tex]\sf A=2((5)(6)+(8)(6)+(8)(5))[/tex]
[tex]\sf A=236~ft^2[/tex]

This is incorrect, they have the same volume of 240 cubic feet and the same surface areas.

B:

Rectangular Prism #1
[tex]\sf V=lwh[/tex]
[tex]\sf V=(8)(5)(6)=240~ft^3[/tex]

[tex]\sf A=2(wl+hl+hw)[/tex]
[tex]\sf A=2((8)(5)+(6)(5)+(6)(8))[/tex]
[tex]\sf A=236~ft^2[/tex]

Rectangular Prism #2
[tex]\sf V=lwh[/tex]
[tex]\sf V=(10)(8)(3)=240~ft^3[/tex]

[tex]\sf A=2(wl+hl+hw)[/tex]
[tex]\sf A=2((10)(8)+(3)(8)+(3)(10))[/tex]
[tex]\sf A=268~ft^2[/tex]

[tex]\boxed{\sf Correct~Answer}[/tex]: Both have the same volume of 240 cubic feet, but different surface areas.

C:

Rectangular Prism #1
[tex]\sf V=lwh[/tex]
[tex]\sf V=(15)(8)(2)=240~ft^3[/tex]

[tex]\sf A=2(wl+hl+hw)[/tex]
[tex]\sf A=2((15)(8)+(2)(8)+(2)(15))[/tex]
[tex]\sf A=332~ft^2[/tex]

Rectangular Prism #2
[tex]\sf V=lwh[/tex]
[tex]\sf V=(6)(4)(15)=360~ft^3[/tex]

[tex]\sf A=2(wl+hl+hw)[/tex]
[tex]\sf A=2((6)(4)+(15)(4)+(15)(6))[/tex]
[tex]\sf A=348~ft^2[/tex]

This is incorrect, they have different surface areas, but only Rectangle #1 has a volume of 240 cubic feet.

D:

Rectangular Prism #1
[tex]\sf V=lwh[/tex]
[tex]\sf V=(12)(6)(5)=360~ft^3[/tex]

[tex]\sf A=2(wl+hl+hw)[/tex]
[tex]\sf A=2((12)(6)+(5)(6)+(5)(12))[/tex]
[tex]\sf A=324~ft^2[/tex]

Rectangular Prism #2
[tex]\sf V=lwh[/tex]
[tex]\sf V=(8)(10)(3)=240~ft^3[/tex]

[tex]\sf A=2(wl+hl+hw)[/tex]
[tex]\sf A=2((8)(10)+(3)(10)+(3)(8))[/tex]
[tex]\sf A=268~ft^2[/tex]

This is incorrect, they both have different surface areas but only Rectangle #2 has a volume of 240 cubic feet.