How many cubic centimetres of iron are there in an open box whose external dimension 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 g, find the weight of the empty box in kg.
Answers
Given : External dimensions of box are 36 cm, 25 cm and 16.5 cm, the iron being 1.5 cm thick throughout and 1 cubic cm of iron weighs 15 g.
Volume of cuboid (box) = length × breadth × height
External volume of a box = (36 × 25 × 16.5) cm
Thickness of iron = 1.5 cm
Inner length = 36 - 2 × 1.5 = 36 - 3 = 33 cm
Inner breadth = 25 - 2 × 1.5 = 25 - 3 = 23 cm
Inner height = 16.5 - 1.5 = 15 cm
Inner volume of a box = (33 × 22 ×15) cm
Volume of iron used , V = External volume – Internal volume
V = (36 × 25 × 16.5) cm – (33 × 22 × 15) cm
V = 14850 - 10890
V = 3960 cm³
Volume of iron used = 3960 cm³
∵ weight of 1 cm³ iron = 15 gm
∴ weight of 3960 cm³ iron = 3960 × 15 = 59400 gm = 59400/1000 = 59.4 kg
[1g = 1/1000 kg]
Hence, 3960 cm³ of iron are there in an open box and the weight of the empty box in kg is 59.4 kg.
HOPE THIS ANSWER WILL HELP YOU…..
Similar questions :
Given that 1 cubic cm of marble weighs 0.25 kg, the weight of marble block 28 cm in width and 5 cm thick is 112 kg. Find the length of the block.
https://brainly.in/question/15911147
Half cubic metre of gold-sheet is extended by hammering so as to cover an area of 1 hectare. Find the thickness of the gold-sheet.
https://brainly.in/question/15911145
External volume of the box = 36cm × 25cm × 16.5cm
=
When the thickness of iron sheet is 1.5cm,the internal dimensions of the open iron box will be
(36-3)cm, (25-3)cm, and (16.5-1.5)cm
or 33cm ,22cm and 15cm
Internal volume of the box
= 33cm × 22cm × 15cm =
Volume of iron used = External volume - Internal Volume
=
=
Weight of of iron = 7.5g
Weight of of iron = 7.5 × 3960g = 29700g
Hence, Weight of the box = 29.7kg