Question

12 cm x 9 cm x 6 cm?
17. There is a water storage tank in the area where Kadir lives. The dimensions of the tank are
8 mx 5 mx 4 m. The tank was full in one evening. In the next morning, the water level goes down
by 0.5 m due to some leakage. When Kadir noticed the leakage, he informed his father. His father
immediately reported about the leakage to the concerned authority. The authority repaired the
leakage immediately. Kadir's this timely action saved a lot of water.
(a) Find the capacity of the tank in litres.
(b) How much water is wasted due to leakage?
(c) Here which value did Kadir depict?
[Value Based Questions]​

Answer 1

Given :

1. The dimensions of the water tank

• $\sf{length = 8m}$
• $\sf{width = 5m}$
• $\sf{height = 4m}$

1. The next morning amount of water in tank reduced by 0.5m.

To Find :

• (a) Find the capacity of the tank in litres.
• (b) How much watethes wasted due to leakage?
• (c) Here which value did Kadir depict?

Formula Applied :

${\underline{\boxed{\textsf{Volume of tank }_{\textsf{cuboid}} ={\sf{lbh }}cu.units}}}$

• $\textsf{I = length}$
• $\textsf{w = width}$
• $\textsf{h = height}$

Solution :

$\sf{capacity\:\: of\:\: tank \:\: = length \times width \times height }$

$\longrightarrow 8m \times 5m \times 4m$

${\underline{\boxed{\text{capacity of water tank = }160m^3}}}$

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$\textsf{(a)Find the capacity of tank in litres}$

$\text{ 1 Metre cube = 1000 litres }$

$\longrightarrow 1m^3 = 1000 l$

$\longrightarrow 160m^3 = 160000 l$

$\underline{\boxed{\textsf{Capacity of tank in litres = 160000 litres}}}$

$\textsf{(b) How much water is wasted due to leakage?}$

• The amount water wasted due to leakage can be finded by Reducing the new capacity of water from the total capacity of the water tank.
• height of water in the tank is reduced due to leakage so we have to change the dimension of tank accordance with height of water in tank.

${\underline{\boxed{\sf{capacity\:\: of\:\: tank \:\: = length \times width \times height }}}}$

$\longrightarrow\sf{8m \times 5m \times 0.5m}$

$\underline{\boxed{\textsf{Amount of water leaked = 20}m^3}}$

$\textsf{(c) Here which value did Kadir depict ?}$

Kadir's action in the appropriate times depicts his matured behaviour

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${\text{\underline{\underline{Related formulas :}}}}$

${\sf{\textsf{Volume of Cubiod}}= lbh cu.units}$

${\sf{\textsf{Volume of }}= s^3}$

${\sf{\textsf{Volume of sphere}}= \frac{4}{3}\pi r^3}$

${\sf{\textsf{Volume of Cylinder}}= \pi r^2h}$

${\sf{\textsf{Cone}}= \frac{1}{3}\pi r^2h}$

Answer 2

${\underline{\underline{\bf{Given:}}}}$

• Dimensions of the storage tank: 8 m × 5 m × 4 m.
• The tank with the above dimensions was full in one evening.
• In the next morning, the water level of the tank decreased by 0.5 m due to some leakage.
• A boy, Kadir noticed the leakage and he informed to his father. His timely action had saved a lot of water.

${\underline{\underline{\bf{Need\:to\:find:}}}}$

• (a) The capacity of the water tank (in litres).
• (b) The amount of water wasted due to leakage.
• (c) The value that Kadir depicted.

${\underline{\underline{\bf{Formula\:to\:be\:used:}}}}$

$\underline{\boxed{\sf{{Volume}_{(cuboid)}=lbh\:cu.units}}}$

$\sf{Where,}$

$\:\:\:\:\:\:\bullet{\sf{\:l=length}}$

$\:\:\:\:\:\:\bullet{\sf{\:b=breadth}}$

$\:\:\:\:\:\:\bullet{\sf{\:h=height}}$

${\underline{\underline{\bf{Solution:}}}}$

(a) The capacity of water tank (in litres):

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎According to the given dimensions, we can say that the shape of the water tank is cuboid. So, the capacity of the tank can be found by substituting the given measures in the formula of volume of cuboid.

$\:\:\:\:\:\:\:\implies{\sf{l\times b\times h\:cu.units}}$

$\:\:\:\:\:\:\:\implies{\sf{8\times 5\times 4}}$

$\:\:\:\:\:\:\:\implies{\sf{40\times 4}}$

$\:\:\:\:\:\:\:\implies{\underline{\underline{\sf{160\:{m}^{3}}}}}$

It is also given to find the capacity of water in litres. As we know,

$\:\:\:\:\:\:\:\:\:{\boxed{\sf{1\:{m}^{3}=1,000\: litres}}}$

$\sf{So,}$

$\:\:\:\:\:\:\:\implies{\sf{160\:{m}^{3}=160\times 1000}}$

$\:\:\:\:\:\:\:\implies{\underline{\underline{\sf{\red{1,60,000\: litres}}}}}$

• Therefore, the total capacity of the tank is 1,60,000 litres.

(b) The amount of water wasted due to the leakage:

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎We're given that the level (height) of the water tank had decreased to 0.5 m in the morning. So the amount of water wasted can be found by substituting 0.5 in place of height in the formula of volume of cuboid. (The measures of the length and the breadth, remains the same). Next, by multiplying the volume with 1000 (1 m³ = 1,000 litres), gives us the required answer.

$\:\:\:\:\:\:\:\implies{\sf{l\times b\times h\:cu.units}}$

$\:\:\:\:\:\:\:\implies{\sf{8\times 5\times 0.5}}$

$\:\:\:\:\:\:\:\implies{\sf{40\times 0.5}}$

$\:\:\:\:\:\:\:\implies{\underline{\underline{\sf{20\:{m}^{3}}}}}$

$\sf{Capacity\:in\:litres,}$

$\:\:\:\:\:\:\:\implies{\sf{20\times 1000}}$

$\:\:\:\:\:\:\:\implies{\underline{\underline{\sf{\red{20,000\: litres}}}}}$

• Therefore, the amount of water wasted due to the leakage was 20,000 litres.

(c) The value that Kadir depicted: (VBQ)

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎Here, in this situation, Kadir had depicted the value of saving water. His timely action implies that he had studied about the importance of saving water as the actual amount of water available for human use is very less (approximately 0.0006 % of the whole water found on the earth) and no life is possible without water.

__________________________________________

${\underline{\underline{\bf{Further\: calculations:}}}}$

The amount of water saved by Kadir:

$\implies{\sf{Total\: capacity\:of\:tank-Amount\:of\:water\: wasted}}$

$\implies{\sf{1,60,000-20,000}}$

$\implies{\sf{\purple{\underline{\underline{1,40,000\:litres}}}}}$

• The amount of water saved by Kadir was 1,40,000 litres.