Question

The water from a cylindrical tank of height 12 m and diameter of base 7 m is emptied into two small cubic tanks of equal capacity. The length of the edge of the tank is 7 m. If one tank is completely filled, find the height of water in the second tank.

Answer 1

Hint: First, find the volume of the spherical tank by the formula $V=\pi {{r}^{2}}h$. After that, find the volume of the tank which is completely filled by the formula $V={{a}^{3}}$. Then, find the volume of the tank partially filled by the formula $V=lbh$. As the water from the cylindrical tank is poured into the other two cubical tanks. Then the volume of water in the cylindrical tank will be equal to the sum of the volume of water in both cubical tanks. Equate them and get the height of the water in the second tank.

Complete step by step answer:
Given: - The height of the cylinder $h = 12 m$
The diameter of the cylinder $d = 7 m$
The side length of the cubical tank $= 7 m$
Let the height of water in the second tank be $x$ m.
The volume of the cylindrical tank is given by,
$V=\pi {{r}^{2}}h$
where $r$ is the radius and $h$ is the height of the tank.
Substitute the values in the formula,
$\Rightarrow V=\dfrac{22}{7}\times {{\left( \dfrac{7}{2} \right)}^{2}}\times 12$
Square the term,
$\Rightarrow V=\dfrac{22}{7}\times \dfrac{49}{4}\times 12$
Cancel out the common factors from the numerator and denominator,
$\Rightarrow V=22\times 7\times 3$
Multiply the terms,
$\Rightarrow V=462{{\text{m}}^{3}}$
The volume of cubical tanks is given by
$V={{a}^{3}}$
where $a$ is the side length of the cube.
Substitute the value in the above formula,
$\Rightarrow V={{7}^{3}}$
Cube the value on the right side,
$\Rightarrow V=343{{\text{m}}^{3}}$
Since the other cubical box has also the same side length 7 m but the height of the water is unknown.
Then the volume of the other cubical tank is given by,
$V=lbh$
where $l$ is the length,$b$ is the breadth, and $h$ is the height.
Substitute the values,
$\Rightarrow V=7\times 7\times h$
Multiply the terms on the right side,
$\Rightarrow V=49x$
As the water from the cylindrical tank is poured into the other two cubical tanks. Then the volume of water in the cylindrical tank will be equal to the sum of the volume of water in both cubical tanks
$\Rightarrow 49x+343=462$
Move the constant part on the right side,
$\Rightarrow 49x=462-343$
Subtract 343 from 462,
$\Rightarrow 49x=119$
Divide both sides by 49,
$\Rightarrow x=2.43\text{m}$

Hence, the height of water in the second tank is 2.43 m.

Note:
The surface area and volume are calculated for any three-dimensional geometrical shape. The surface area of any given object is the area or region occupied by the surface of the object. Whereas volume is the amount of space available in an object.
Generally, Area can be of two types:
Total surface area: Total surface area refers to the area including the base(s) and the curved part. It is a total of the area covered by the surface of the object.
Curved surface area/Lateral surface area: Curved surface area refers to the area of only the curved part of the shape excluding its base(s). It is also referred to as a lateral surface area.
Volume: The amount of space, measured in cubic units, that an object or substance occupies is called volume. Two-dimensional doesn’t have volume but has area only.