NCERT Class 9 Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.9

NCERT Solutions for Class 9 Maths Chapter 13  – Surface Areas and Volumes Topics and Sub Topics

  • Surface Areas And Volumes
  • Introduction
  • Surface Area of a Cuboid and a Cube
  • Surface Area of a Right Circular Cylinder
  • Surface Area of a Right Circular Cone
  • Surface Area of a Sphere
  • Volume of a Cuboid
  • Volume of a Cylinder
  • Volume of a Right Circular Cone
  • Volume of a Sphere
  • Summary

Surface Areas and Volumes Class 9 Maths Formulas

NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.9

Ex 13.9 Class 9 Maths Question 1.
A wooden bookshelf has external dimensions as follows : Height = 110cm, Depth = 25cm, Breadth = 85cm (see figure). The thickness of the plank is 5 cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing-is 20 paise per cm2 and the rate of pointing is 10 paise per cm2, find the total expenses required for palishing and painting the surface of the bookshelf.
NCERT Class 9 Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.9 A1
Solution:
Here, l = 85 cm b = 25 cm and h = 110 cm
Area of the bookshelf of outer surface = 2 lb + 2bh + hl
= [2(85 x 25)+ 2(110 x 25)+ 85×110] cm2 = (4250 + 5500 + 9350) cm2 = 19100 cm2
Cost of polishing of the outer surface of bookshelf
= 19100 x \(\frac { 20 }{ 100 }\) = ₹ 3820
Thickness of the plank = 5 cm
Internal height of bookshelf = (110 – 2 x 5) = 100 cm
Internal depth of bookshelf = (25 – 5) = 20 cm
Internal breadth of bookshelf = 85 – 2 x 5 = 75 cm
Hence, area of the internal surface of bookshelf
= 2(75 x 20)+ 2(100x 20)+ 75×100
= 3000 + 4000 + 7500 = 14500 cm2
So, cost of painting of internal surface of bookshelf
= 14500 x \(\frac { 10 }{ 100 }\) = ₹1450
Hence, total costing of polishing and painting = 3820 + 1450= ₹ 5270

Ex 13.9 Class 9 Maths Question 2.
The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in figure. Eight such spheres are-used for this purpose, and are to be painted silver. Each support is a cylinder of radius 1.5 cm and height 7 cm and is to be painted black. Find the cost of paint required if silver paint costs 25 paise per cm2 and black paint costs 5 paise per cm2.
NCERT Class 9 Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.9 A2
Solution:
It is obvious, we have to subtract the cost of the sphere that is resting on the supports while calculating the cost of silver paint.
Surface area to be silver paint
NCERT Class 9 Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.9 A2.1

Ex 13.9 Class 9 Maths Question 3.
The diameter of a sphere is decreased by 25%. By what per cent does its curved surface area decrease?
Solution:
Let d be the diameter of the sphere
NCERT Class 9 Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.9 A3

NCERT Class 9 Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.9 A3.1

NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes (Hindi Medium) Ex 13.9

9 Maths Chapter 13 Exercise 13.9 optional exercises solutions
9 Maths Chapter 13 Exercise 13.9 download in pdf free
Class 9 Maths Chapter 13 Exercise 13.9 optional exercises in pdf
Class 9 Maths Chapter 13 Exercise 13.9 all questions guide free
Class 9 Maths Chapter 13 Exercise 13.9 solutions for up, mp, gujrat and cbse board

NCERT Solutions for Class 9 Maths

  1. Chapter 1 Number systems
  2. Chapter 2 Polynomials
  3. Chapter 3 Coordinate Geometry
  4. Chapter 4 Linear Equations in Two Variables
  5. Chapter 5 Introduction to Euclid Geometry
  6. Chapter 6 Lines and Angles
  7. Chapter 7 Triangles
  8. Chapter 8 Quadrilaterals
  9. Chapter 9 Areas of Parallelograms and Triangles
  10. Chapter 10 Circles
  11. Chapter 11 Constructions
  12. Chapter 12 Heron’s Formula
  13. Chapter 13 Surface Areas and Volumes
  14. Chapter 14 Statistics
  15. Chapter 15 Probability
  16. Class 9 Maths (Download PDF)