Question

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 ft

B) 8 ft by 5 ft by 6 ft and 10 ft by 8 ft by 3 ft

C) 15 ft by 8 ft by 2 ft and 6 ft by 4 ft by 15 ft

D) 12 ft by 6 ft by 5 ft and 8 ft by 10 ft by 3 ft

Answer 1

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

A:

Rectangular Prism #1

`\sf V=lwh`

`\sf V=(8)(5)(6)=240~ft^3`


`\sf A=2((8)(5)+(6)(5)+(6)(8))`

`\sf A=236~ft^2`

Rectangular Prism #2

`\sf V=lwh`

`\sf V=(5)(6)(8)=240~ft^3`


`\sf A=2((5)(6)+(8)(6)+(8)(5))`

`\sf A=236~ft^2`

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

B:

Rectangular Prism #1

`\sf V=lwh`

`\sf V=(8)(5)(6)=240~ft^3`


`\sf A=2(wl+hl+hw)`

`\sf A=2((8)(5)+(6)(5)+(6)(8))`

`\sf A=236~ft^2`

Rectangular Prism #2

`\sf V=lwh`

`\sf V=(10)(8)(3)=240~ft^3`


`\sf A=2(wl+hl+hw)`

`\sf A=2((10)(8)+(3)(8)+(3)(10))`

`\sf A=268~ft^2`


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

C:

Rectangular Prism #1

`\sf V=lwh`

`\sf V=(15)(8)(2)=240~ft^3`


`\sf A=2(wl+hl+hw)`

`\sf A=2((15)(8)+(2)(8)+(2)(15))`

`\sf A=332~ft^2`

Rectangular Prism #2

`\sf V=lwh`

`\sf V=(6)(4)(15)=360~ft^3`


`\sf A=2(wl+hl+hw)`

`\sf A=2((6)(4)+(15)(4)+(15)(6))`

`\sf A=348~ft^2`

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

D:

Rectangular Prism #1

`\sf V=lwh`

`\sf V=(12)(6)(5)=360~ft^3`


`\sf A=2(wl+hl+hw)`

`\sf A=2((12)(6)+(5)(6)+(5)(12))`

`\sf A=324~ft^2`

Rectangular Prism #2

`\sf V=lwh`

`\sf V=(8)(10)(3)=240~ft^3`


`\sf A=2(wl+hl+hw)`

`\sf A=2((8)(10)+(3)(10)+(3)(8))`

`\sf A=268~ft^2`

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