An open tank 15 m long, 12 m wide and 5 m deep is to be constructed with the help of a stainless-steel sheet which is 1.5 m in width. What length (in m) of the sheet will be required?

Options

A. 350
B. 450
C. 250
D. 300

Answer

To determine the length of the stainless-steel sheet required to construct the open tank, we need to follow these steps:

### Step 1: Calculate the Surface Area of the Open Tank
The open tank has a length (L), width (B), and height (H). The formula for the surface area (SA) of an open tank (which has no top) is given by:

\[ SA = L \times B + 2 \times (L \times H + B \times H) \]

Where:
- \(L = 15 \, m\) (length)
- \(B = 12 \, m\) (width)
- \(H = 5 \, m\) (height)

### Step 2: Substitute the Values into the Formula
Substituting the values into the surface area formula:

\[ SA = 15 \times 12 + 2 \times (15 \times 5 + 12 \times 5) \]

### Step 3: Calculate Each Component
Now, calculate each term:
- \(15 \times 12 = 180\)
- \(15 \times 5 = 75\)
- \(12 \times 5 = 60\)

Now, substitute these values back into the surface area equation:

\[ SA = 180 + 2 \times (75 + 60) \]

### Step 4: Simplify the Equation
Calculate the sum inside the parentheses:

\[ 75 + 60 = 135 \]

Now, multiply by 2:

\[ 2 \times 135 = 270 \]

Finally, add this to the area of the base:

\[ SA = 180 + 270 = 450 \, m^2 \]

### Step 5: Calculate the Length of the Stainless-Steel Sheet Required
The width of the stainless-steel sheet is given as 1.5 m. To find the length of the sheet required, we can use the formula:

\[ \text{Length of sheet} = \frac{\text{Total Surface Area}}{\text{Width of sheet}} \]

Substituting the values:

\[ \text{Length of sheet} = \frac{450}{1.5} \]

### Step 6: Perform the Division
Now, perform the division:

\[ \text{Length of sheet} = 300 \, m \]

### Final Answer
The length of the stainless-steel sheet required to construct the open tank is **300 meters**.

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