Question:
How many cubic centimeters of iron are there in an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm, the iron being 1.5 cm thick throughout? If 1 cubic cm of iron weighs 15 gms. Find the weight of the empty box in kg.
Solution:
Given,
Outer dimensions of iron:
Length (l) = 36 cm
Breadth (b) = 25 cm
Height (h) = 16.5 cm
Inner dimensions of iron:
Length (l) = 36 - (2*1.5) = 33 cm
Breadth (b) = 25 - (2*1.5) = 22 cm
Height (h) = 16.5 - 1.5 = 15 cm
Volume of Iron = Outer volume – Inner volume
= (36 * 25 * 16.5) – (33 * 22 * 15)
$=3960 \mathrm{~cm}^{3}$
Weight of Iron = 3960 * 15 = 59400 grams = 59.4 kgs