Question

Which shows the dimensions of two rectangular prisms that have volumes of 240 ft3 but different surface areas?

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.