Question

Which has the greater surface area? A 6-centimeter cube or a rectangular prism with a 3 centimeter square base and a height of 12 centimeters?

Answer 1

Answer:

The prism

Step-by-step explanation:

The surface area of a cube is:

$A=6L^2$

where

L is the length of the side

For the cube in this problem,

L = 6 cm

So the surface area of the cube is

$A=6\cdot 6^2 = 36 cm^2$

The surface area of a rectangular prism with squared base is:

$A=2L^2+4Lh$

where

L is the length of the base

h is the height of the prism

For the prism in this problem,

L = 3 cm

h = 12 cm

Therefore,

$A=2\cdot 3^2 + 4(3)(12)=162 cm^2$

So, the prism has a greater surface area.