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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

Respuesta :

Answer:

(A)[tex]420$ cm^3[/tex]

Step-by-step explanation:

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

Volume of the solid box [tex]= 10*6*15=900$ cm^3[/tex]

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[tex]=8*4*15=480$ cm^3[/tex]

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

=900-480

=[tex]420$ cm^3[/tex]

The correct option is A.

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