Question

The external dimensions of an open wooden
box are 65 cm, 34 cm and 25 cm. If the box is
made up of wood 2 cm thick, find the capacity
of the box and the volume of wood used to
make it.
​

Answer 1

65 - 4 = 63

34 - 2 = 32

25 - 2 = 23

63 x 32 x 23 = 46368

The capacity of the box is 46368 sq.cm

65 x 34 x 25 = 55250

55250 - 46368 = 8882

8882 sq.cm wood used to make the box

Answer 2

$\sf \Large Solution!!$

$\sf \large Given,$

$\sf \to External\;length\;of\;the\;open\;box=65\;cm$

$\sf \to External\;breadth\;of\;the\;open\;box=34\;cm$

$\sf \to External\;height\;of\;the\;open\;box=25\;cm$

$\sf \to Thickness\;of\;wood=2\;cm$

$\sf \large So,$

$\sf \to External\;volume\;of\;the\;open\;box=length\times breadth\times height$

$\sf \to External\;volume\;of\;the\;open\;box=65\;cm\times 34\;cm\times 25\;cm=55250\;cm^{3}$

$\sf \large Now,$

$\sf \to Internal\;length\;of\;open\;box=65-(2\times 2)\;cm=61\;cm$

$\sf \to Internal\;breadth\;of\;open\;box=34-(2\times 2)\;cm=30\;cm$

$\sf \to Internal\;height\;of\;open\;box=25-2\;cm=23\;cm$

$\sf \large So,$

$\sf \to Internal\;volume\;of\;open\;box=length\times breadth\times height$

$\sf \to Internal\;volume\;of\;open\;box=61\;cm\times 30\;cm\times 23\;cm=42090\;cm^{3}$

$\sf \large So,$

$\sf \to Volume\;of\;wood\;required\;to\;make\;the\;closed\;box=55250\;cm^{3}-42090\;cm^{3}=13160\;cm^{3}$

$\sf \boxed{\bigstar The\;capacity\;of\;the\;box\;and\;the\;volume\;of\;wood\;used\;to\;make\;it=42090cm^{3}\;and\;13160cm^{3}}$