Math  /  Geometry

Question4.2 To irrigate a soccer field, a special cylindrical watercart is used. The tank is 3,5 m3,5 \mathrm{~m} long and has a diameter of 200 cm .
Refer to the picture and information above to answer the questions that follow. 4.2.1 Calculate the amount of water (in litres) when the water tank is full.
You may use the following formula: Volume =π×( radius )2×=\pi \times(\text { radius })^{2} \times length Use: π=3,142\boldsymbol{\pi}=3,142 Also note that: 1000 cm3=11000 \mathrm{~cm}^{3}=1 litre and 1 m3=10001 \mathrm{~m}^{3}=1000 litres 4.2.2 The water tank is made of a metal sheet. Calculate the amount (in square metres) of metal used to make a water tank. Round your answer to two decimal places. You may use the formula: Surface area =2×π×=2 \times \pi \times radius (radius + length) Use: π=3,142\pi=3,142

Studdy Solution

STEP 1

1. The watercart tank is a cylinder.
2. The length of the cylinder is 3.5m3.5 \, \text{m}.
3. The diameter of the cylinder is 200cm200 \, \text{cm}.
4. π\pi is approximated as 3.1423.142.
5. Conversion factors: 1000cm3=1litre1000 \, \text{cm}^3 = 1 \, \text{litre} and 1m3=1000litres1 \, \text{m}^3 = 1000 \, \text{litres}.

_HIGH_LEVEL_APPROACH_ for 4.2.1:
1. Convert all measurements to consistent units.
2. Calculate the volume of the cylinder.
3. Convert the volume to litres.

_HIGH_LEVEL_APPROACH_ for 4.2.2:
1. Convert all measurements to consistent units.
2. Calculate the surface area of the cylinder.
3. Round the surface area to two decimal places.

STEP 2

STEP 3

Convert the diameter to radius in meters:
Diameter=200cm=2m \text{Diameter} = 200 \, \text{cm} = 2 \, \text{m} Radius=Diameter2=2m2=1m \text{Radius} = \frac{\text{Diameter}}{2} = \frac{2 \, \text{m}}{2} = 1 \, \text{m}

STEP 4

Calculate the volume of the cylinder using the formula:
V=π×(radius)2×length V = \pi \times (\text{radius})^2 \times \text{length} =3.142×(1m)2×3.5m = 3.142 \times (1 \, \text{m})^2 \times 3.5 \, \text{m}

STEP 5

Calculate the volume:
V=3.142×1×3.5 V = 3.142 \times 1 \times 3.5 =11.007m3 = 11.007 \, \text{m}^3
Convert the volume to litres:
11.007m3×1000litres/m3=11007litres 11.007 \, \text{m}^3 \times 1000 \, \text{litres/m}^3 = 11007 \, \text{litres}

STEP 6

Convert the radius and length to consistent units for surface area calculation:
Radius=1m \text{Radius} = 1 \, \text{m} Length=3.5m \text{Length} = 3.5 \, \text{m}

STEP 7

Calculate the surface area of the cylinder using the formula:
Surface Area=2×π×radius×(radius+length) \text{Surface Area} = 2 \times \pi \times \text{radius} \times (\text{radius} + \text{length}) =2×3.142×1×(1+3.5) = 2 \times 3.142 \times 1 \times (1 + 3.5)

STEP 8

Calculate the surface area:
Surface Area=2×3.142×1×4.5 \text{Surface Area} = 2 \times 3.142 \times 1 \times 4.5 =28.278m2 = 28.278 \, \text{m}^2
Round the surface area to two decimal places:
Surface Area28.28m2 \text{Surface Area} \approx 28.28 \, \text{m}^2
The amount of water the tank can hold when full is:
11007litres \boxed{11007 \, \text{litres}}
The amount of metal used to make the tank is:
28.28m2 \boxed{28.28 \, \text{m}^2}

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