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The length of cold storage is double its breadth. Its height is 3 meters. If the area of four walls including doors is 108 m^{2}, what is its volume?
Let l = 2b, h = 3m
Area of four walls = 108
2 (l + b) h = 108
⇒ 2 (2b + b) 3 = 108
⇒ 3b = 108/6 = 18
⇒ b = 18/3 = 6
∴ l = 2b = 2 × 6 = 12
∴ Volume of cold storage
= lbh = 12 × 6 × 3 = 216 m^{3}
The paint in a certain container is sufficient to paint an area of 9.375 m^{2}. How many bricks of dimension 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?
No. of bricks
A solid cube is cut into two cuboids of equal volumes. Find the ratio of total surface area of given cube and that of one cuboid.
Volume of cuboid = a^{3}/2 = Ibh
∴ Surface area of each cuboid
= 2 (lb + bh + lh)
= 2 (2a^{2}) = 4a^{2}
Total surface area of cube = 6a^{2}
∴ Required ratio = 6a^{2} : 4a^{2} = 3 : 2
The diameter of the roller 1.5 m long is 84 cm. If it takes 100 revolutions to level a playground, what is the cost of leveling the playground at the rate of 50 paise per square meter?
The curved surface area of the roller = 2πrh
= 44 × 150 × 6
Area covered by roller in 100 revolutions
Cost of leveling the playground
= ₹ 198
The volume of a cylinder is 448 π cm^{3} and height 7 cm. What is the lateral surface area of the cylinder?
Volume of the cylinder = 448π
⇒ πr^{2}h = 448π
⇒ r^{2}h = 448
⇒ r = 8 cm
Lateral surface area = 2πrh
= 22 × 16 = 352 cm^{2}
At a meal, a stall keeper in one of the food stalls has a large cylindrical vessel of base radius 15cm filled up to a height of 32 cm with fruit juice. The juice is filled in small cylindrical glasses of radius 3cm up to a height of 8cm. how many glasses will be filled by selling the juice completely?
Let the number of glasses be n
∴ Total volume in the vessel = volume of juice in glasses
⇒ πR^{2}H = n × πr^{2}h
⇒ R^{2}H = nr^{2}h
⇒ (15)^{2} × 32 = n × (3)^{2} × 8
⇒ n = 5 × 5 × 4 = 100
How many meters of cloth of 5 m width will be required to make a conical tent. The radius of whose base is 7 m and heights is 24 m?
Curved surface = πrl = 22/7 × 7 × 25 = 550 m^{2}
Length of canvas used
The diameter of the moon is approximately 1/4th of the diameter of the earth. What fraction of the volume of earth is the volume of the moon?
Let the diameter of the earth be x m
∴ Diameter of moon = x/4 m
Water flows in a tank 150 m × 100 m at the base through a pipe whose crosssection is 2 dm by 1.5 dm at the speed of 15 km per hour. At what time will the water be 3 meters deep?
The volume of water in the tank
= 150 × 100 × 3 = 45000 m^{3}
Area of a crosssection of the pipe
= 2dm × 1.5dm
Let the time taken be t hours.
The volume of water that flows in a tank in t hours.
= 450 t m^{3}
⇒ 450t = 45000
⇒ t = 45000/450 = 100 hours
In a shower, 5cm of rainfalls. What is the volume of water that falls on 2 hectares of the ground?
Volume of water
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