"Question 7 A lead pencil consists of a cylinder of wood with solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.
Class 9 - Math - Surface Areas and Volumes Page 231"
Answers
VOLUME:
The space occupied by an object solid body is called the volume of the particular object solid body volume is always measured in cubic unit.
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Solution:
Given:
Diameter of the pencil =7mm
Radius of the pencil (R) = 7/2mm
Diameter of the graphite cylinder =1mm
Radius of the graphite(r) = 1/2mm
Height(h)=14cm= 140mm
[1cm= 10 mm]
Volume of a cylinder= πr²h
Volume of graphite cylinder = πr2h = 22/7 ×1/2 × 1/2 ×140
Volume of graphite = 110 mm³
Volume of pencil = πR²h
= 22/7 ×7/2 × 7/2 ×140
= 490×11= 5390 mm²
Volume of pencil=5390mm³
Volume of wood = Volume of pencil - Volume of graphite
Volume of wood= 5390- 110= 5280 mm³
= 5280/1000= 5.28 cm³
[1mm³= 1/1000cm³]
Volume of wood = 5.28 cm³
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Hope this will help you...
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•volume of graphite =πr^2h
= 22/7×1/20×1/20×14
=0.11 cm^3
•volume of pencil = πR^2h
= 22/7×7/20×7/20×14
=5.39 cm ^3
•volume of wood = volume of pencil - volume of graphite
= 5.39-0.11
= 5.28 cm ^3
for the diagram refer to the attachment
hope helped
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