Question

A box tube is to be constructed out of 1 cm thick metal that has a width of 10cm, a height of 6cm, and a depth of 15 cm. Which of the following represents the volume of the metal used?

(1) 420 cm3 (3) 640 cm3
(2) 540 cm3 (4) 760 cm3

Answer 1

(A)
`420$ cm^3`

Explanation:

• Width = 10cm
• Height = 6cm
• Depth = 15 cm

Volume of the solid box
`= 10*6*15=900$ cm^3`

Since the box tube is constructed out of 1 cm thick metal, we subtract 1cm on both sides of the width and height.

See the attached diagram for illustration.

• Internal width of the box = 10-2=8cm
• Internal height of the box = 6-2=4cm

However, the depth of the box remains unchanged, therefore:

• Internal depth of the box =15cm

Internal Volume of the box
`=8*4*15=480$ cm^3`

Volume of metal used = Volume of Solid Box - Internal Volume

=900-480

=
`420$ cm^3`

The correct option is A.