Surface Areas and Volumes: 9 Math
NCERT Exemplar Exercise 13.3 Q6-10: 9th math
Solution of NCERT Exemplar Exercise 13.3 Surface Areas And Volumes Class 9 Math Question (6) A school provides milk to the students daily in a cylindrical glasses of diameter 7 cm. If the glass is filled with milk upto an height of 12cm, find how many litres of milk is needed to serve 1600 students.
Solution
Given, diameter of the cylindrical glass = 7 cm
Thus, radius of the glass = 7/2 = 3.5 cm
And, height of the milk in the glass = 12 cm
And, number of students = 1600
Thus, Litre of milk required daily for all the students = ?
Here, the volume of milk required for one student = volume of milk in one cylindrical glass up to the given height
We know that, Volume of a cylinder = ℼ r2 h
Thus, volume of the milk in the given cylindrical glass
= ℼ (3.5 cm)2 × 12 cm
= `22/7` 3.5 cm × 3.5 cm × 12 cm
= 22 × 0.5 cm × 3.5 cm × 12 cm
= 22 × 21 cm3
= 462 cm3
Thus, volume of the milk for one student
= 462 cm3
= 462/1000 = 0.462 Litre
Thus, volume of the milk for 1600 students
= 0.462 Litre × 1600 = 739.200 Litre
Thus, milk required to serve all the given students daily = 739.200 Litre Answer
Solution of NCERT Exemplar Exercise 13.3 Surface Areas And Volumes Class 9 Math Question (7) A cylindrical roller 2.5 m in length, 1.75 m in radius when rolled on a road was found to cover the area of 5500 m2 . How many revolutions did it make?
Solution
Given, length of the cylindrical roller = 2.5 m
And, the radius of the given cylindrical roller = 1.75 m
And, area covered by the given roller = 5500 m2
Thus, number of revolution to cover the given area by the roller = ?
Here, area covered by the roller in one revolution = curved surface area of the roller
We know that Curved Surface Area of a Cylinder
= 2 ℼ r h
Thus, curved surface area of the given roller = 2 ℼ 1.75 m × 2.5 m
= ℼ × 2 × 1.75 m × 2.5 m
= `22/7` × 3.5 m × 2.5 m
= 22 × 0.5 m × 2.5 m
= 22 × 1.25 m2
= 27.5 m2
Thus, curved surface area of the given roller = 27.5 m2
Thus, area covered by the roller in one revolution = 27.5 m2
Now, since number of revolution to cover 27.5 m2 by the given roller = 1
Thus, to cover 1 m2, the number of revolution = 1/27.5 m2
Thus, to cover 5500 m2, the number of revolution `=1/(27.5 m^2)xx5500m^2`
= 200 revolution
Thus, to cover the given area the number of revolution made by given roller
= 200 Answer
Solution of NCERT Exemplar Exercise 13.3 Surface Areas And Volumes Class 9 Math Question (8) A small village, having a population of 5000, requires 75 litres of water per head per day. The village has got an overhead tank of measurement 40 m × 25 m × 15 m . For how many days will the water of this tank last?
Solution
Given, Population = 5000
Consumption of water per head per day = 75 `l`
And, Length of the water tank (`l`) = 40 m
And, Breadth of the water tank (b) = 25 m
And, Height of the water tank (h) = 15 m
Thus, number of days for which water is sufficient in the given tank = ?
Now, we know that, Volume of a cuboid `=lxxbxxh`
Therefore, volume of the given cuboidal tank =
= 40 m × 25 m × 15 m
= 1000 m2 × 15 m
= 15000 m3
Thus, volume of the tank = 15000 m3
Calculation of water sufficient for how many days
Now, we know that, 1 m3 = 1000 Litre
Therefore, 15000 m3 = 15000000 Litre
And, since, as per question, consumption of water per head per day = 75 Litre and population of the village is equal to 5000
Therefore, in 1 day consumption of water for whole population = 5000 × 75 Litre
Thus, per day consumption of water = 375000 Litre
Now volume of water in the tank = 15000000 Litre
Now, since 375000 litres of water last for 1 day
Therefore, 1 litre of water last for `1/375000` days
Therefore, 15000000 litres of water last for `1/375000xx15000000` days
= 40 days
Thus, water in the tank will last for 40 days Answer
Solution of NCERT Exemplar Exercise 13.3 Surface Areas And Volumes Class 9 Math Question (9) A shopkeeper has one spherical laddoo of radius 5 cm. With the same amount of material, how many laddoos of radius 2.5 cm can be made?
Solution
Given, radius of one laddoo = 5 cm
Thus, number of laddoos of radius 2.5 cm can be made from the material of that laddoo = ?
Here, a laddoo has a spherical shape.
Thus, number of laddoos of radius 2.5 cm = volume of laddoos of radius 5 cm/volume of laddoos of radius 2.5 cm
Now, we know that, Volume of a sphere = 4/3 ℼ r3
Number number of laddoos of radius 2.5 cm
`=(4/3xxpi\ (5cm)^3)/(4/3xxpi\(2.5cm)^3)`
= 125 cm / 6.25 cm
= 8 Laddoos
Thus, number of given small laddoos made by given big laddoo = 8 Answer
Solution of NCERT Exemplar Exercise 13.3 Surface Areas And Volumes Class 9 Math Question (10) A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. Find the volume and the curved surface of the solid so formed.
Solution
Given, sides of the right angled triangle = 6 cm, 8 cm and 10 cm
And, the given right angled triangle is revolved around the side of 8 cm
Thus, volume and curved surface area of solid cone so formed = ?
Here, since, the given right angled triangle is revolved about the side 8 cm
Thus, radius of the solid cone so formed = 6 cm
And, height of the solid cone so formed = 8 cm
And, slant height of the solid cone so formed = 10 cm
Now, we know that, Volume of a cone = 1/3 ℼ r2 h
Thus, volume of the given cone formed in the question
= `1/3xx22/7` × (6 cm)2 × 8 cm
= `22/21` × 36 cm2 × 8 cm
= `22/21` 288 cm3
= 301.71 cm3
Thus, volume of the solid cone formed as per question = 301.71 cm2
Now, we know that Curved Surface Area of a Cone = ℼ r l
Thus, curved surface area of the given cone
= `22/7` 6 cm × 10 cm
= `22/7` 60 cm2
= 188.571 cm2
Thus, volume of the cone = 301.71 cm3 and curved surface area of the cone formed = 188.571 cm2 Answer
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