Question

A farmer has a water tank for cows in the shape of a cylinder with radius of 1.4m and height of 2 m. The tank comes equipped with a sensor to alert the farmer to fill it up when the water falls to 20% capacity.
(i) Find the curve surface area of tank
(i) What is the volume of the tank when the sensor turns on?(use π = 22/7)

Answer 1

Answer:

For part 2 first find the volume and then 20% of the total volume

i.e., volume= πr²h

= 22/7 × 1.4 × 1.4 × 2

= 56×22/100= 12.32 m³

Now 20% 9f the original volume

i.e., 20/100 × 12.32 = 2.464 m³ when the sensor turns on.

Answer 2

• The curved surface area of the water tank is equal to 17.6 m² .
• The volume of the tank when the sensor turns on is equal to 2.464 m³ .

Given :-

• Radius of cylinder = 1.4 m
• Height of cylinder = 2 m
• The tank comes equipped with a sensor to alert the farmer to fill it up when the water falls to 20% capacity.

To Find :-

(i) The curved surface area of tank

(ii) The volume of the tank when the sensor turns on ?

Formula used :-

• Curved surface area of cylinder = 2 × π × radius × height .
• Volume of cylinder = π × radius × radius × height
• π = (22/7)

Solution :-

given that,

→ Radius of water tank = r = 1.4 m

→ Height of water tank = h = 2 m

(i)

So,

→ CSA of the water tank = 2πrh

putting given values,

→ CSA of the water tank = 2 × (22/7) × 1.4 × 2

→ CSA of the water tank = 2 × 22 × 0.2 × 2

→ CSA of the water tank = 44 × 0.4

→ CSA of the water tank = 17.6 m² (Ans.)

(ii)

→ Volume of the water tank = πr²h

putting given values,

→ Volume of the water tank = (22/7) × 1.4 × 1.4 × 2

→ Volume of the water tank = 22 × 0.2 × 1.4 × 2

→ Volume of the water tank = 4.4 × 2.8

→ Volume of the water tank = 12.32 m³

Now, given that, the sensor alert the farmer to fill it up when the water falls to 20% capacity.

therefore,

→ The volume of the tank when the sensor turns on = 20% of the volume of the water tank

→ Required volume = (20 × 12.32)/100

→ Required volume = 2.464 m³ (Ans.)

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