Find the depth of a cylindrical tank of radius 10.5 cm, if its capacity is equal to that of a rectangular tank of size 15 cm x 11 cm x 10.5 cm.

Answer

To find the depth (height) of a cylindrical tank with a radius of 10.5 cm, given that its capacity (volume) is equal to that of a rectangular tank with dimensions 15 cm x 11 cm x 10.5 cm, we can follow these steps:

### Step 1: Calculate the volume of the rectangular tank.
The volume \( V \) of a rectangular tank can be calculated using the formula:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
Given:
- Length = 15 cm
- Breadth = 11 cm
- Height = 10.5 cm

Substituting the values:
\[ V = 15 \times 11 \times 10.5 \]

### Step 2: Perform the multiplication.
Calculating the volume:
\[ V = 15 \times 11 = 165 \]
Now, multiply by 10.5:
\[ V = 165 \times 10.5 = 1732.5 \text{ cm}^3 \]

### Step 3: Set the volume of the cylindrical tank equal to the volume of the rectangular tank.
The volume \( V \) of a cylindrical tank is given by the formula:
\[ V = \pi r^2 h \]
Where:
- \( r \) is the radius (10.5 cm)
- \( h \) is the height (depth) we need to find

Setting the volumes equal:
\[ \pi r^2 h = 1732.5 \]

### Step 4: Substitute the radius into the equation.
Substituting \( r = 10.5 \):
\[ \pi (10.5)^2 h = 1732.5 \]
Calculating \( (10.5)^2 \):
\[ (10.5)^2 = 110.25 \]
So the equation becomes:
\[ \pi \times 110.25 \times h = 1732.5 \]

### Step 5: Substitute the value of \( \pi \).
Using \( \pi \approx \frac{22}{7} \):
\[ \frac{22}{7} \times 110.25 \times h = 1732.5 \]

### Step 6: Solve for \( h \).
First, multiply \( \frac{22}{7} \) by \( 110.25 \):
\[ \frac{22 \times 110.25}{7} = \frac{2425.5}{7} = 346.5 \]
Now, the equation is:
\[ 346.5h = 1732.5 \]
To find \( h \), divide both sides by 346.5:
\[ h = \frac{1732.5}{346.5} = 5 \text{ cm} \]

### Final Answer:
The depth of the cylindrical tank is **5 cm**.

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