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The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood has a mass of 0.6 g.
Since the cylindrical wooden pipe is made up of two concentric circles at the top and bottom, we will find the volume of both cylinders.
The volume of a cylinder of base radius, r, and height, h = πr2h
The volume of wood can be obtained by finding the difference between the volumes of both the outer and inner cylinders.
Outer diameter of the pipe = 28 cm
Outer radius of the pipe, R = 28/2 = 14 cm
Inner diameter of the pipe = 24 cm
Inner radius of the pipe, r = 24/2 = 12cm
Length of the pipe, h = 35 cm
Volume of the outer cylinder, V1 = π R2 h
V1 = 22/7 × 14cm × 14cm × 35cm
= 21560 cm3
Volume of the inner cylinder, V2 = πr2h
V2 = 22/7 × 12cm × 12cm × 35cm
= 15840 cm3
The volume of the wood used = Volume of the outer cylinder – Volume of the inner cylinder
= 21560 cm3 - 15840 cm3
= 5720 cm3
Mass of 1 cm3 wood is 0.6 g
Mass of 5720 cm3 wood = 5720 × 0.6g
= 3432 g
= (3432/1000) kg
= 3.432 kg
Thus, the mass of the wooden pipe is 3.432 kg
The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm³ of wood has a mass of 0.6 g.
NCERT Solutions for Class 9 Maths Chapter 13 Exercise 13.6 Question 2
It is given that the inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. If the length of the pipe is 35 cm, and 1 cm³ of wood has a mass of 0.6 g, the total mass of the wooden pipe is 3.432 kg.
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