*According to the CBSE Syllabus 2023-24, this chapter has been renumbered as Chapter 11.
NCERT Solutions for Class 9 Maths Chapter 13 – Surface Areas and Volumes Exercise 13.1, include the solved problems from the NCERT textbook. The solutions are available in PDF format, and students can download them easily. The NCERT solutions are created by Maths subject experts, along with proper geometric figures and explanations in a step-by-step procedure for good understanding.
The collection of all the solutions in NCERT Solutions for Class 9 Maths is as per the latest NCERT syllabus and guidelines of the CBSE board, and it aims to help the students to score good marks in the board examinations.
Download PDF of NCERT Solutions for Class 9 Maths Chapter 13 – Surface Areas and Volumes Exercise 13.1
Access other exercise solutions of Class 9 Maths Chapter 13 – Surface Areas and Volumes
Exercise 13.2 solution (8 questions)
Exercise 13.3 solution (9 questions)
Exercise 13.4 solution (5 questions)
Exercise 13.5 solution (5 questions)
Exercise 13.6 solution (8 questions)
Exercise 13.7 solution (9 questions)
Exercise 13.8 solution (10 questions)
Exercise 13.9 solution (3 questions)
Access answers of Maths NCERT Class 9 Maths Chapter 13 – Surface Areas and Volumes Exercise 13.1
1. A plastic box 1.5 m long, 1.25 m wide, and 65 cm deep is to be made. It is to be open at the top. Ignoring the thickness of the plastic sheet, determine:
(i) The area of the sheet required for making the box.
(ii) The cost of the sheet for it, if a sheet measuring 1m2 costs Rs. 20.
Solution:
Given: length (l) of box = 1.5m
Breadth (b) of box = 1.25 m
Depth (h) of box = 0.65m
(i) Box is to be open at the top.
Area of sheet required.
= 2lh+2bh+lb
= [2×1.5×0.65+2×1.25×0.65+1.5×1.25]m2
= (1.95+1.625+1.875) m2 = 5.45 m2
(ii) Cost of sheet per m2 area = Rs.20.
Cost of sheet of 5.45 m2 area = Rs (5.45×20)
= Rs.109
2. The length, breadth and height of a room are 5 m, 4 m and 3 m, respectively. Find the cost of whitewashing the walls of the room and ceiling at the rate of Rs 7.50 per m2.
Solution:
Length (l) of room = 5m
Breadth (b) of room = 4m
Height (h) of room = 3m
It can be observed that four walls and the ceiling of the room are to be whitewashed.
Total area to be whitewashed = Area of walls + Area of the ceiling of the room
= 2lh+2bh+lb
= [2×5×3+2×4×3+5×4]
= (30+24+20)
= 74
Area = 74 m2
Also,
Cost of whitewash per m2 area = Rs.7.50 (Given)
Cost of whitewashing 74 m2 area = Rs. (74×7.50)
= Rs. 555
3. The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of Rs.10 per m2 is Rs.15000, find the height of the hall.
[Hint: Area of the four walls = Lateral surface area]
Solution:
Let the length, breadth, and height of the rectangular hall be l, b, and h, respectively.
Area of four walls = 2lh+2bh
= 2(l+b)h
Perimeter of the floor of hall = 2(l+b)
= 250 m
Area of four walls = 2(l+b) h = 250h m2
Cost of painting per square meter area = Rs.10
Cost of painting 250h square meter area = Rs (250h×10) = Rs.2500h
However, it is given that the cost of painting the walls is Rs. 15000.
15000 = 2500h
Or h = 6
Therefore, the height of the hall is 6 m.
4. The paint in a certain container is sufficient to paint an area equal to 9.375 m2. How many bricks of dimensions 22.5 cm×10 cm×7.5 cm can be painted out of this container?
Solution:
Total surface area of one brick = 2(lb +bh+lb)
= [2(22.5×10+10×7.5+22.5×7.5)] cm2
= 2(225+75+168.75) cm2
= (2×468.75) cm2
= 937.5 cm2
Let n bricks can be painted out by the paint of the container.
Area of n bricks = (n×937.5) cm2 = 937.5n cm2
As per the given instructions, the area that can be painted by the paint of the container = 9.375 m2 = 93750 cm2
So, we have 93750 = 937.5n
n = 100
Therefore, 100 bricks can be painted out by the paint of the container.
5. A cubical box has each edge 10 cm, and another cuboidal box is 12.5cm long, 10 cm wide, and 8 cm high.
(i) Which box has the greater lateral surface area, and by how much?
(ii) Which box has the smaller total surface area, and by how much?
Solution:
From the question statement, we have
Edge of a cube = 10cm
Length, l = 12.5 cm
Breadth, b = 10cm
Height, h = 8 cm
(i) Find the lateral surface area for both figures.
Lateral surface area of cubical box = 4 (edge)2
= 4(10)2
= 400 cm2 …(1)
Lateral surface area of cuboidal box = 2[lh+bh]
= [2(12.5×8+10×8)]
= (2×180) = 360
Therefore, the lateral surface area of the cuboidal box is 360 cm2. …(2)
From (1) and (2), the lateral surface area of the cubical box is more than the lateral surface area of the cuboidal box. The difference between both lateral surfaces is 40 cm2.
(Lateral surface area of the cubical box – Lateral surface area of cuboidal box=400cm2–360cm2 = 40 cm2)
(ii) Find the total surface area for both figures.
The total surface area of the cubical box = 6(edge)2 = 6(10 cm)2 = 600 cm2…(3)
The total surface area of the cuboidal box
= 2[lh+bh+lb]
= [2(12.5×8+10×8+12.5×100)]
= 610
This implies that the total surface area of the cuboidal box is 610 cm2..(4)
From (3) and (4), the total surface area of the cubical box is smaller than that of the cuboidal box. And their difference is 10cm2.
Therefore, the total surface area of the cubical box is smaller than that of the cuboidal box by 10 cm2
6. A small indoor greenhouse (herbarium) is made entirely of glass panes (including the base) held together with tape. It is 30cm long, 25 cm wide, and 25 cm high.
(i) What is the area of the glass?
(ii) How much tape is needed for all 12 edges?
Solution:
The length of the greenhouse, say l = 30cm
The breadth of the greenhouse, say b = 25 cm
Height of greenhouse, say h = 25 cm
(i) Total surface area of greenhouse = Area of the glass = 2[lb+lh+bh]
= [2(30×25+30×25+25×25)]
= [2(750+750+625)]
= (2×2125) = 4250
The total surface area of the glass is 4250 cm2
(ii)
From the figure, the tape is required along sides AB, BC, CD, DA, EF, FG, GH, HE AH, BE, DG, and CF.
Total length of tape = 4(l+b+h)
= [4(30+25+25)] (after substituting the values)
= 320
Therefore, 320 cm tape is required for all 12 edges.
7. Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions 25 cm×20cm×5cm, and the smaller of dimensions 15cm×12cm×5cm. For all the overlaps, 5% of the total surface area is required extra. If the cost of the cardboard is Rs. 4 for 1000 cm2, find the cost of cardboard required for supplying 250 boxes of each kind.
Solution:
Let l, b and h be the length, breadth and height of the box, respectively.
Bigger Box:
l = 25cm
b = 20 cm
h = 5 cm
Total surface area of bigger box = 2(lb+lh+bh)
= [2(25×20+25×5+20×5)]
= [2(500+125+100)]
= 1450 cm2
Extra area required for overlapping 1450×5/100 cm2
= 72.5 cm2
While considering all overlaps, the total surface area of the bigger box
= (1450+72.5) cm2 = 1522.5 cm2
Area of cardboard sheet required for 250 such bigger boxes
= (1522.5×250) cm2 = 380625 cm2
Smaller Box:
Similarly, total surface area of smaller box = [2(15×12+15×5+12×5)] cm2
= [2(180+75+60)] cm2
= (2×315) cm2
= 630 cm2
Therefore, the extra area required for overlapping 630×5/100 cm2 = 31.5 cm2
The total surface area of 1 smaller box while considering all overlaps
= (630+31.5) cm2 = 661.5 cm2
Area of cardboard sheet required for 250 smaller boxes = (250×661.5) cm2 = 165375 cm2
In Short:
| Box | Dimensions (in cm) | Total surface area (in cm2 ) | Extra area required for overlapping (in cm2) | Total surface area for all overlaps (in cm 2) | Area for 250 such boxes (in cm2) |
| Bigger Box | l = 25
b = 20 c = 5 |
1450 | 1450×5/100
= 72.5 |
(1450+72.5) = 1522.5 | (1522.5×250) = 380625 |
| Smaller Box | l = 15
b = 12 h =5 |
630 | 630×5/100 = 31.5 | (630+31.5) = 661.5 | ( 250×661.5) = 165375 |
Now, total cardboard sheet required = (380625+165375) cm2
= 546000 cm2
Given: Cost of 1000 cm2 cardboard sheet = Rs. 4
Therefore, the cost of 546000 cm2 cardboard sheet =Rs. (546000×4)/1000 = Rs. 2184
Therefore, the cost of cardboard required for supplying 250 boxes of each kind will be Rs. 2184.
8. Praveen wanted to make a temporary shelter for her car by making a box-like structure with a tarpaulin that covers all four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5m, with base dimensions 4m×3m?
Solution:
Let l, b and h be the length, breadth and height of the shelter, respectively.
Given:
l = 4m
b = 3m
h = 2.5m
A tarpaulin will be required for the top and four wall sides of the shelter.
Using the formula, the area of tarpaulin required = 2(lh+bh)+lb
On putting the values of l, b and h, we get
= [2(4×2.5+3×2.5)+4×3] m2
= [2(10+7.5)+12]m2
= 47m2
Therefore, 47 m2 of tarpaulin will be required.
Exercise 13.1 of Class 9 maths consists of problems which cover the concepts like the surface area of a cube and cuboid. It involves the application level of real-time problems that push students to think and apply the relevant formula.
It also explains how six rectangular pieces are used to cover the complete outer surface of the cuboid and how the surface area of a cuboid and cube is found.
Learn the entire NCERT Solutions for Class 9 Maths Chapter 13, along with other learning materials and notes provided by BYJU’S. The problems are solved in a detailed way with relevant formulas and figures to score well in the CBSE exams.
Key Features of NCERT Solutions for Class 9 Maths Chapter 13 – Surface Areas and Volume Exercise 13.1
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