Passage

A city community centre has developed a rainwater storage system to reduce its dependence on municipal water. The system consists of different tanks and containers of standard geometrical shapes. The main underground storage tank is a cuboid measuring 8 metres in length, 5 metres in breadth and 3 metres in height. During normal operations, this tank is usually filled only up to 75% of its total capacity.

Alongside the main tank, the centre has a cylindrical tank with a radius of 2 metres and a height of 3.5 metres. For temporary storage, several smaller cuboidal containers are also available, each measuring 2 metres × 2 metres × 1 metre.

Before rainwater enters the storage system, it passes through a conical filtration chamber having a radius of 1.4 metres and a vertical height of 3 metres. The filtered water can then be transferred to either of the storage tanks.

For all calculations, take π = 22/7 and remember that 1 cubic metre = 1,000 litres.

Question 1

What is the combined total capacity of the main cuboidal tank and the cylindrical tank?

A. 144 m³
B. 154 m³
C. 160 m³
D. 164 m³

Question 2

How much water is stored in the main cuboidal tank when it is filled to 75% of its total capacity?

A. 90 m³
B. 80 m³
C. 100 m³
D. 120 m³

Question 3

How many smaller cuboidal containers would be required to store the entire quantity of water that can be held by the cylindrical tank?

A. 9
B. 10
C. 11
D. 12

Question 4

What is the total capacity of the conical filtration chamber in litres?

A. 5,160 litres
B. 6,160 litres
C. 6,600 litres
D. 7,160 litres

Question 5

Suppose the cylindrical tank is initially half-filled. If the conical filtration chamber is completely filled with water and all of that water is transferred to the cylindrical tank, what will be the total volume of water in the cylindrical tank?

A. 24.16 m³
B. 26.16 m³
C. 28.16 m³
D. 30.16 m³

Answers and Detailed Explanations

Question 1 – Answer: D. 164 m³

Volume of a cuboid:

Volume = Length × Breadth × Height

Therefore,

= 8 × 5 × 3
= 120 m³

Now, volume of the cylindrical tank:

Volume = πr²h

= 22/7 × 2² × 3.5

= 22/7 × 4 × 3.5

= 44 m³

Therefore, combined capacity:

= 120 + 44
= 164 m³

Hence, Option D is correct.

Question 2 – Answer: A. 90 m³

The total capacity of the main cuboidal tank is:

= 8 × 5 × 3
= 120 m³

The tank is filled to 75% of its capacity.

Therefore, water stored:

= 75/100 × 120

= 90 m³

Hence, Option A is correct.

Question 3 – Answer: C. 11

First, calculate the capacity of one smaller cuboidal container:

= Length × Breadth × Height

= 2 × 2 × 1

= 4 m³

The capacity of the cylindrical tank is:

= 44 m³

Therefore, number of smaller containers required:

= 44 ÷ 4

= 11 containers

Hence, Option C is correct.

Question 4 – Answer: B. 6,160 litres

Volume of a cone:

Volume = 1/3 × πr²h

Given:

Radius = 1.4 m
Height = 3 m

Therefore,

Volume = 1/3 × 22/7 × 1.4 × 1.4 × 3

The 3 in the numerator and denominator cancel out.

= 22/7 × 1.96

= 6.16 m³

Since:

1 m³ = 1,000 litres

Therefore,

6.16 × 1,000 = 6,160 litres

Hence, Option B is correct.

Question 5 – Answer: C. 28.16 m³

The total capacity of the cylindrical tank is:

= 44 m³

Since it is initially half-filled:

Water already present = 44 ÷ 2

= 22 m³

The conical filtration chamber contains:

= 6.16 m³

After transferring this water to the cylindrical tank:

= 22 + 6.16

= 28.16 m³

Therefore, the cylindrical tank will contain 28.16 m³ of water.

Hence, Option C is correct.