How many cubic centimetres of iron is required to construct an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm provided the thickness of the iron is 1.5 cm. If one cubic cm of iron weighs 7.5 g, find the weight of the box
Solution:
Given, an open box has an external dimension of 36 cm, 25 cm and 16.5 cm.
Open box is made of iron.
The thickness of the iron is 1.5 cm
We have to find the volume of iron required to construct the open box.
We have to find the weight of the box if one cubic cm of iron weighs 7.5 g.
Let the thickness of iron be x.
Given, x = 1.5 cm
External volume of an open box = length × breadth × height
= 36 × 25 × 16.5
= 14850 cm³
Internal length of box = length - 2x
= 36 - 2(1.5)
= 36 - 3
= 33 cm
Internal breath of box = breadth - 2x
= 25 - 2(1.5)
= 25 - 3
= 22 cm
Internal height of box = height - x
= 16.5 - 1.5
= 15 cm
Internal volume of box = (length - 2x) × (breadth - 2x) × (height - x)
= 33 × 22 × 15
= 10890 cm³
Volume of iron required to construct an open box = external volume - internal volume
= 14850 - 10890
= 3960 cm³
Therefore, the volume of iron required to construct an iron box is 3960 cm³.
Given, weight of 1 cm³ iron = 7.5 g
Weight of 3960 cm³ of iron = 7.5(3960)
= 29700 g
1 kg = 1000 g
So, weight of 3960 cm³ of iron = 29700/1000
= 29.7 kg
Therefore, the weight of iron required to construct an open box is 29.7 kg.
✦ Try This: How many cubic centimetres of iron is required to construct an open box whose external dimensions are 24 cm, 19 cm and 10 cm provided the thickness of the iron is 0.8 cm. If one cubic cm of iron weighs 9 g, find the weight of the box.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13
NCERT Exemplar Class 10 Maths Exercise 12.4 Problem 3
How many cubic centimetres of iron is required to construct an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm provided the thickness of the iron is 1.5 cm. If one cubic cm of iron weighs 7.5 g, find the weight of the box
Summary:
3960 cubic centimetres of iron is required to construct an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm provided the thickness of the iron is 1.5 cm. If one cubic cm of iron weighs 7.5 g, the weight of the box is 29.7 kg
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