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

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

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

NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.9 are the part of NCERT Solutions for Class 9 Maths. Here you can find the NCERT Solutions for Chapter 13 Surface Areas and Volumes Ex 13.9.


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 = 110 cm, Depth = 25 cm, Breadth = 85 cm (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 painting is 10 paise per cm2, find the total expenses required for polishing and painting the surface of the bookshelf.


Solution:
Here, length (l) = 85 cm, breadth (b) = 25 cm and height (h) = 110 cm
External surface area = Area of four faces + Area of back + Area of front beading
= [2 (110 + 85) × 25 + 110 × 85 + (110 × 5 × 2) + (75 × 5) × 4] cm2 = 21700 cm2
Cost of polishing external faces = Rs. (21700 × 20/10) = Rs. 4340
Internal surface area = Area of five faces of 3 cuboids each of dimensions 75 cm × 30 cm × 20 cm

= Total surface area of 3 cuboids of dimensions 75 cm × 30 cm × 20 cm – Area of bases of 3 cuboids of dimensions 75 cm × 30 cm × 20 cm

= 3(2(75 × 30 + 30 × 20 + 75 × 20)) cm2 – 3 × (75 × 30) cm2
= 6(2250 + 600 + 1500) cm2 – 6750 cm2 = 19350 cm2
Cost of painting inner faces = Rs. 19350 × 10/100 = Rs. 1935
Here, total expenses = Rs. (4340 + 1935) = Rs. 6275

 

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.


Solution:
Here, diameter of a sphere = 21 cm
Radius of a sphere (r) = 21/2 cm
Surface area of a sphere = 4πr2

Surface area of 8 spheres
= 8 × 4 × 22/7 × (21/2)2 cm2

Hence, the cost of paint required = Rs. 2784.25

 

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 the diameter of the sphere be d.
After decreasing, diameter of the sphere
= d – 25/100 × d
= d – ¼ d = ¾ d
Since, surface area of a sphere = 4πr2 or π(2r)2 or πd2
Surface area of a sphere, when diameter of the sphere is

Now, percentage decrease in curved surface area


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