Wednesday, 15 September 2021 06:44

# 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
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)