Volume, Capacity and Mass - Class 8 Mathematics Revision Notes

Volume, Capacity and Mass

Worked Exercises

1. A Jerry can contains 5 litres of juice. This juice is used to fill 3 containers each of radius 7 cm and height of 10cm. How many milliliters of juice are left in the jerry can?
   1. 38
   2. 480 
   3. 400
   4. 420
      Working
      Volume of container: = Πr² h
      =²²/₇ x 7 x 7 x 10
      = 1540 cm³
      Volume of 3 such containers
      = (1540x3) cm³
      = 4620 cm³
      Volume of juice in jerry can = (5 x 1000)
      = 5000cm³
      Volume of juice left = (5000-4620) cm3
      = 380 cm³
      = 380 ml
      The correct answer is A (380ml)
2. The diagram below represents a solid whose dimensions are shown.
   
   What is the volume in cm³?
   1. .30000
   2. 300000
   3. 3000
   4. 3000000
      Working
      Volume = Area of the Cross-section x length
      Volume of the top = (20 x 10 x 150)
      = 30,000cm³
      Volume of the bottom = 60 x 30 x150
      = 270,000cm³
      Whole solid = top + bottom
      = 30,000 + 270,000
      = 300,000cm³
      The correct answer is B (300 000)
3. In the month of October, a farmer delivered 48750kg of maize to a miller. In November the amount of maize delivered was 1850kg more than that of October. The amount delivered in December was 2450kg less than that of November. What was the total mass, in tonnes, was delivered by the farmer in the 3 months?
   1. 145.65
   2. 147.5
   3. 152.4
   4. 150.55
      Working
      October = 48750 kg
      November = (48750+1850) kg
      = 50,600 kg
      December = 50,600-2,450) kg
      = 48,150 kg
      Total mass = 48750+50600 +48150
      = (147500/1000) tonnes
      = 147.5 tonnes.
      The correct answer is B (147.5)
4. A rectangular tank measures 1.2m by 80cm by 50cm. water is poured into the tank to a height of 15cm. How many more liters of water are needed to fill the tank?
   1. 144
   2. 14.4
   3. 33.6
   4. 336
      Working
      Capacity of the tank = 120 x 80 x 50
      = 480,000cm³
      Convert to litres = ^480,000/¹⁰⁰⁰
      = 480litres
      Volume of the water poured = 120 x 80 x 50
      = 144000cm³
      Convert to litres = ¹⁴⁴⁰⁰⁰/₁₀₀₀
      = 144 litres
      Volume of water needed = 480 – 144 = 366litres.
      The correct answer is D (366)
5. The diagram below represents a solid triangular prism.
   
   What is the volume in cm³?
   1. 2400
   2. 2000
   3. 5200
   4. 576
      Working
      Apply Pythagorean relation in triangle ABC
      BC =√26² -10²
      =√576
      = 24cm
      Volume = Area of the Cross section x length
      = ½ x 24 x 10x 20
      = 2400cm³
      The correct answer is A (2400cm³)
6. A cylindrical tank has a radius of 2m and a height of 1.5m. The tank was filled with water to a depth of 0.5M. What is the volume of water in the tank, in litres? (П = 3.14)
   1. 6280
   2. 628 
   3. 9240
   4. 18840
      Working
      Volume = П r ²h
      = 3.14 x 2 x 2 x 0.5
      = 6.28 m³
      In litres = (6.28 x1000) litres
      = 6280 litres
      The correct answer A (6280)
7. When processed, 7kg of coffee beans produce 1kg of processed coffee. Processed coffee is then packed in 50kg bags. A farmer delivered 5.6 tonnes of coffee berries in one month. How many bags were obtained?
   1. 12
   2. 16
   3. 40
   4. 20
      Working
      Mass of coffee berries = 5.6tonnes
      = 5.6x1000
      = 5600kg
      Mass obtained = ⁵⁶⁰⁰/₇
      = 800kg
      Number of bags = 800 ÷ 50
      = 16 bags
      The correct answer is B (16)
8. A rectangular container whose base measures 40cm by 60cm has 30 liters of water when full. Find the height of the container in cm.
   
   1. 0125
   2. 1.25
   3. 12.5
   4. 125
      Working
      V = base area x height
      Height = ^volume/_{base area}
      Volume = 30 litres
      = 30x1000
      = 30,000cm³
      Height = ^30,000/₂₄₀₀
      = 12.5cm
      The correct answer is C (12.5)
9. A shopkeeper had 43 litres sand 5 litres and 5 dl of paraffin. He packed all the paraffin in 7.5 dl-containers. How many containers did he fill?
   1. 58
   2. 5.8
   3. 6
   4. 60
      Working
      Convert decilitres into litres
      1 dl =1/10 litres
      5 dl =5/10 litres
      7.5 dl =7.5/10 litres = 0.75 litres
      Hence 43 litres 5dl = 43.5 litres
      No of containers = ^43.5/_0.75 = 58 containers
      The correct answer is 58 (A)
10. The figure below shows a cylindrical solid of diameter 28cm and length 20 cm. A square hole of side 1.5 cm has been removed. What is the volume of the material in the solid, in 3cm³?
    
    1. 12320
    2. 4500
    3. 8400
    4. 7820
       Working
       
       Volume of solid = volume of a cylinder - volume of the square hole
       = ( x 14 x 14x 20) - (15 x 15 x 20)
       = 12320 - 4500
       = 7,820 cm³
       The correct answer is D (7,820cm³)