Question

The area of the base of a rectangular tank is $6500c{{m}^{2}}$ and then the volume of water contained in it is \[2.6\text{ }cubic\text{ }meter\]. The depth of water in the tank is:

A) \[3.5m\]

B) \[4m\]

C) \[5m\]

E) \[6m\]

Answer 1

Hint: Here, we will use the formula of the Volume of the Cuboid is =($l\times b\times h$) to find the volume of the tank. And next the formula for the area of the rectangle is =($l\times b$) to find the base area of the tank. Also, the units given to the terms are different; therefore first convert them in the common unit system.

Complete step-by-step solution:

Given: Area of base of tank =$6500c{{m}^{2}}$

 Volume of water contained in it is\[=2.6\text{ }cubic\text{ }meter\].

As we know that 

$ 1m=100cm $

$  \Rightarrow 1{{m}^{2}}=100cm\times 100cm $

$ \Rightarrow 1{{m}^{2}}={{10}^{4}}c{{m}^{2}} $

Now, the required answer should be meters. Convert area of the base in meter square.

$  10000c{{m}^{2}}=1{{m}^{2}} $

$  6500c{{m}^{2}}=? $

$  \Rightarrow \dfrac{6500\times 1}{10000} $

$ \Rightarrow 0.65{{m}^{2}} $

Therefore, area of the tank is $=0.65{{m}^{2}}$

Volume of water tank in tank= $2.6{{m}^{3}}$.

Depth of the water tank is

$\Rightarrow \dfrac{volume\text{ }of\text{ }water\text{ }in\text{ }tank}{base\text{ }area\text{ }of\text{ }tank}=\dfrac{2.6{{m}^{3}}}{0.65{{m}^{2}}} $

$\Rightarrow \dfrac{volume\text{ }of\text{ }water\text{ }in\text{ }tank}{base\text{ }area\text{ }of\text{ }tank}=\dfrac{260}{65}m $

( Multiplying and dividing the ratio by hundred )

Simplification implies-

$\dfrac{volume\text{ }of\text{ }water\text{ }in\text{ }tank}{base\text{ }area\text{ }of\text{ }tank}=4m$

Therefore, the depth of the water tank is $=4m$.

Hence, option B is the correct answer.

Note:Here, we will first convert both area and volume in the same unit of measurement that is meter. The height of the water tank is considered here as depth for the water stored in the tank. In such types of problems, we divide the volume of the tank by base area; it will give us the required height or depth of the container. We need to be very keen about the shape while selecting the formula to find the volume, slant height, the curved surface area or the total surface area. As the tank has the rectangular base so, it is a cuboid tank.