Surface Areas and Volumes is an important chapter in Class 9 Mathematics that helps students understand the 3D geometry and properties of various solid shapes. This chapter covers key topics such as surface area and volume of cubes, cuboids, cylinders, cones, spheres, and hemispheres, along with the formulae used to calculate these quantities. It is crucial for solving 3D geometry problems in school exams and competitive exams.
Q.
A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is opened 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 sheet for it, if a sheet measuring 1m2 costs ₹ 20.
Q.
Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per m3.
Q.
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.
Q.
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.
Q.
Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S′. Find the
(i) radius r ′ of the new sphere,
(ii) ratio of S and S′.
Q.
A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of ₹ 498.96. If the cost of white-washing is ₹ 2.00 per square metre, find the
(i) inside surface area of the dome,
(ii) volume of the air inside the dome.
Q.
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.
Q.
A village, having a population of 4000, approximately requires 150 litres of water per head per day. It has a tank measuring 20 m × 15 m × 6 m. For how many days will the water of this tank last?
Q.
The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m.
Q.
A right circular cylinder just encloses a sphere of radius r (see Figure). Find
(i) surface area of the sphere,
(ii) curved surface area of the cylinder,
(iii) ratio of the areas obtained in (i) and (ii).
Q.
The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of ₹ 7.50 per m2.
Q.
In Figure, you see the frame of lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of 20 cm and height of 30 cm. A margin of 2.5 cm is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade.
Q.
A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of Rs 12.50 per m2.
Q.
The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in m2.
Q.
A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4 cm (figure shown below) . Find its
(i) inner curved surface area,
(ii) outer curved surface area,
(iii) total surface area.
Q.
The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the diameter of the base of the cylinder
Q.
A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm 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?
Q.
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?
Q.
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, fin the height of the hall.
Q.
Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find
(i) radius of the base
(ii) total surface area of the cone.
NCERT Solutions for Class 9 Maths Chapter 11 – Surface Areas and Volumes are prepared strictly according to the latest CBSE syllabus and exam pattern. The solutions are written in simple, step-by-step language with clear explanations, formulae, and solved examples, helping students grasp concepts quickly and solve problems efficiently.
NCERT Solutions for Class 9 Maths Chapter 11 – Surface Areas and Volumes
Q. 1) Find the cost of digging a cuboidal pit 8 m long, 6 m broad, and 3 m deep at the rate of Rs 30 per m³.
Answer:
Volume of cuboidal pit = 8 × 6 × 3 = 144 m³
Cost of digging 1 m³ pit = Rs. 30
Then, the cost of digging the cuboidal pit = Rs. 30 × 144 = Rs. 4320
Thus, the cost of digging the cuboidal pit is Rs. 4320.
Q. 2) The capacity of a cuboidal tank is 50,000 liters of water. Find the breadth of the tank if its length and depth are respectively 2.5 m and 10 m.
Answer:
Capacity of cuboidal tank = 50,000 liters
Length of cuboidal tank = 2.5 m
Depth of cuboidal tank = 10 m
Let breadth of the cuboidal tank = p m
Since, 1000 liters = 1 m³, so 50,000 liters = 50 m³
Then, Volume of the tank = l × b × h = 50 m³
50 = 2.5 × p × 10
p = 2 m
Thus, the breadth of the tank is 2 m.
Q. 3) A village, having a population of 4000, approximately requires 150 liters of water per head per day. It has a tank measuring 20 m × 15 m × 6 m. For how many days will the water in this tank last?
Answer:
Volume of the water tank = 20 m × 15 m × 6 m = 1800 m³ = 1,800,000 liters (since 1 m³ = 1000 liters)
Water required for a person = 150 liters
Water required for 4000 persons = 150 × 4000 liters = 600,000 liters
Number of days the water in the tank will last = 1,800,000 / 600,000 = 3 days
Thus, the water in the tank will last for 3 days in a village of 4000 people.
Q. 4) Curved surface area of a cone is 308 cm², and its slant height is 14 cm. Find
(i) the radius of the base
(ii) the total surface area of the cone.
Answer:
(i) Curved surface area of the cone = 308 cm²
Formula: π × r × l = 308 cm²
(22/7) × r × 14 = 308 cm²
r = (308 / 14) × (7 / 22) = 7 cm
Thus, the radius of the base of the cone is 7 cm.
(ii) Total surface area of the cone = π × r × (l + r)
= (22/7) × 7 × (14 + 7)
= 22 × 21 = 462 cm²
Thus, the total surface area of the cone is 462 cm².
FAQs: Class 9 Maths Chapter 11 – Surface Areas and Volumes
Q1. Is Surface Areas and Volumes important for Class 9 exams?
Yes, it is an important and scoring chapter with numerous formulae-based numericals.
Q2. What topics are most important in this chapter?
Surface area and volume of cubes, cuboids, cylinders, spheres, cones, and hemispheres.
Q3. Are numericals asked in this chapter?
Yes, surface area and volume problems are frequently asked in exams.
Q4. How do you calculate the surface area and volume of a cone?
Surface Area of Cone = πr(l + r)
Volume of Cone = (1/3)πr²h, where r is the radius and h is the height.
Q5. How do NCERT Solutions help?
They provide step-by-step solutions with detailed explanations and examples to help solve problems accurately.