### Volume, Capacity and Mass

Worked Exercises

- 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?
- 38
- 480
- 400
- 420

Working

Volume of container: = Πr^{2}h

=^{22}/_{7}x 7 x 7 x 10

= 1540 cm^{3}Volume of 3 such containers

= (1540x3) cm^{3}

= 4620 cm^{3}Volume of juice in jerry can = (5 x 1000)

= 5000cm^{3}Volume of juice left = (5000-4620) cm3

= 380 cm^{3}= 380 ml

The correct answer is A (380ml)

- The diagram below represents a solid whose dimensions are shown.

What is the volume in cm^{3}?- .30000
- 300000
- 3000
- 3000000

Working

Volume = Area of the Cross-section x length

Volume of the top = (20 x 10 x 150)

= 30,000cm^{3}Volume of the bottom = 60 x 30 x150

= 270,000cm^{3}Whole solid = top + bottom

= 30,000 + 270,000

= 300,000cm^{3}The correct answer is B (300 000)

- 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?
- 145.65
- 147.5
- 152.4
- 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)

- 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?
- 144
- 14.4
- 33.6
- 336

Working

Capacity of the tank = 120 x 80 x 50

= 480,000cm^{3}Convert to litres =^{480,000}/^{1000}= 480litres

Volume of the water poured = 120 x 80 x 50

= 144000cm^{3}Convert to litres =^{144000}/_{1000}= 144 litres

Volume of water needed = 480 – 144 = 366litres.

The correct answer is D (366)

- The diagram below represents a solid triangular prism.

What is the volume in cm^{3}?- 2400
- 2000
- 5200
- 576

Working

Apply Pythagorean relation in triangle ABC

BC =√26^{2}-10^{2}

=√576

= 24cm

Volume = Area of the Cross section x length

= ½ x 24 x 10x 20

= 2400cm^{3}The correct answer is A (2400cm^{3})

- 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)
- 6280
- 628
- 9240
- 18840

Working

Volume = П r^{2}h

= 3.14 x 2 x 2 x 0.5

= 6.28 m^{3}In litres = (6.28 x1000) litres

= 6280 litres

The correct answer A (6280)

- 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?
- 12
- 16
- 40
- 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)

- A rectangular container whose base measures 40cm by 60cm has 30 liters of water when full. Find the height of the container in cm.
- 0125
- 1.25
- 12.5
- 125

Working

V = base area x height

Height =^{volume}/_{base area}Volume = 30 litres

= 30x1000

= 30,000cm^{3}Height =^{30,000}/_{2400}= 12.5cm

The correct answer is C (12.5)

- 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?
- 58
- 5.8
- 6
- 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)

- 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 3cm
^{3}?- 12320
- 4500
- 8400
- 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 cm^{3}The correct answer is D (7,820cm^{3})

Join our whatsapp group for latest updates

Tap Here to Download for 30/-

Get on WhatsApp for 30/-

#### Download Volume, Capacity and Mass - Class 8 Mathematics Revision Notes.

Tap Here to Download for 30/-

Get on WhatsApp for 30/-

#### Why download?

- ✔ To read offline at any time.
- ✔ To Print at your convenience
- ✔ Share Easily with Friends / Students