Question

Which expressions show the volume and the surface area of this cube-shaped packing box?

Math item stem image
CLEAR CHECK

=(135)3 in.3; =3·(135)2 in.2
V
=
13
5
3

i
n
.
3
;

S
A
=
3
·
13
5
2

i
n
.
2


=(135)3 in.3; =6·(135)2 in.2
V
=
13
5
3

i
n
.
3
;

S
A
=
6
·
13
5
2

i
n
.
2


=6·(135)3 in.3; =(135)2 in.2
V
=
6
·
13
5
3

i
n
.
3
;

S
A
=
13
5
2

i
n
.
2


=3·(135)3 in.3; =6·(135)2 in.2

Answer 1

The volume =
`((13)/(8))^3`
`feet^3` and Surface area is
`6((13)/(8))^2`
`feet^2`

Explanation:

Given:

The side of the cube =
`1(5)/(8)` feet

To Find:

volume = ?

surface area = ?

Solution:

Step 1: Finding the surface area of the cube shaped packing box

We know that the volume of the cube is

=>
`6a^2`

On Substituting the value

surface area of the box

=>
`6(1(5)/(8))`

=>
`6((8 + 5)/(8))^2`

=>
`6((13)/(8))^2`
`feet^2`

Step 1: Finding the volume of the cube shaped packing box

We know that the volume of the cube is

=>
`(a)^3`

On Substituting the value

Volume of the box

=>
`( 1(5)/(8))^3`

=>
`((8+5)/(8))^3`

=>
`((13)/(8))^3`
`feet^3`