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.
Solution:
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
☛ Check: NCERT Solutions for Class 9 Maths Chapter 13
Video Solution:
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
Summary:
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.
☛ Related Questions:
- A soft drink is available in two packs - (i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm, and (ii) a plastic cylinder with a circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?
- If the lateral surface of a cylinder is 92.4 cm3 and its height is 5 cm, then find(i) radius of its base(ii) its volume. (Use π = 3.14)
- It costs ₹2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of ₹20 per m2, find.(i) inner curved surface area of the vessel,(ii) radius of the base,(iii) capacity of the vessel.
- The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?
visual curriculum