NCERT Solutions for Class 9 Maths Chapter 13
Important NCERT Questions
Surface Areas and Volumes
NCERT Books for Session 2022-2023
CBSE Board, UP Board and Other state Boards
EXERCISE 13.6
Page No:230
Questions No:7
A lead pencil consists of a cylinder of wood with a 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.
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Inner radius of wood in pencil r = 1/2 = 0.5 mm = 0.05 cm,
Outer radius R = 7/2 = 3.5 mm = 0.35 cm and length h = 14 cm
Volume of wood used in pencil = π(R² – r²)h
= 22/7 × [(0.35)² – (0.05)²] × 14
= 22 × (0.1225 – 0.0025) × 2
= 22 × 0.12 × 2
= 5.28 cm³
Radius of graphite inside the wood r = 1/2 = 0.5 mm = 0.05 cm and height h = 14 cm.
Volume of graphite in pencil = πr²h
= 22/7 × (0.05)² × 14
= 22 × 0.0025 × 2
= 0.11 cm³
Hence, in pencil, the volume of wood is 5.28 cm³ and that of graphite is 0.11 cm³.