SITUATION 9:
A vat filled with paint is 9 m long. Its ends are
in the form of trapezoid 3 m at the bottom and
5 m on the top. The vat is 4 m high and the
specific gravity of paint is 0.8 .
50 . Compute the total weight of paint.

Ask by Watson Joseph. in the Philippines

Dec 08,2024

Question

SITUATION 9:
A vat filled with paint is 9 m long. Its ends are
in the form of trapezoid 3 m at the bottom and
5 m on the top. The vat is 4 m high and the
specific gravity of paint is 0.8 .
50 . Compute the total weight of paint.

Ask by Watson Joseph. in the Philippines

Dec 08,2024

UpStudy AI · Accepted Answer

To compute the total weight of the paint in the vat, we first need to find the volume of the vat and then use the specific gravity to find the weight.

### Step 1: Calculate the Volume of the Trapezoidal Vat

The volume $$ V $$ of a trapezoidal prism can be calculated using the formula:

$$
V = A \cdot L
$$

where $$ A $$ is the area of the trapezoidal cross-section and $$ L $$ is the length of the vat.

#### Step 1.1: Calculate the Area of the Trapezoidal Cross-section

The area $$ A $$ of a trapezoid can be calculated using the formula:

$$
A = \frac{1}{2} \cdot (b_1 + b_2) \cdot h
$$

where:
- $$ b_1 $$ is the length of the bottom base (3 m),
- $$ b_2 $$ is the length of the top base (5 m),
- $$ h $$ is the height of the trapezoid (4 m).

Substituting the values:

$$
A = \frac{1}{2} \cdot (3 + 5) \cdot 4 = \frac{1}{2} \cdot 8 \cdot 4 = 16 \, \text{m}^2
$$

#### Step 1.2: Calculate the Volume of the Vat

Now, we can calculate the volume $$ V $$:

$$
V = A \cdot L = 16 \, \text{m}^2 \cdot 9 \, \text{m} = 144 \, \text{m}^3
$$

### Step 2: Calculate the Weight of the Paint

The weight $$ W $$ of the paint can be calculated using the formula:

$$
W = V \cdot \text{Specific Weight}
$$

The specific weight $$ \gamma $$ can be calculated from the specific gravity $$ SG $$:

$$
\text{Specific Weight} = SG \cdot \text{Weight of Water} = 0.8 \cdot 9.81 \, \text{kN/m}^3 = 7.848 \, \text{kN/m}^3
$$

Now, substituting the values to find the weight:

$$
W = V \cdot \text{Specific Weight} = 144 \, \text{m}^3 \cdot 7.848 \, \text{kN/m}^3 = 1131.072 \, \text{kN}
$$

### Final Answer

Rounding to one decimal place, the total weight of the paint is approximately:

$$
W \approx 1130.1 \, \text{kN}
$$

Thus, the correct answer is:

**b. 1130.1 kN**
The total weight of the paint is approximately 1130.1 kN.

SITUATION 9:
A vat filled with paint is 9 m long. Its ends are
in the form of trapezoid 3 m at the bottom and
5 m on the top. The vat is 4 m high and the
specific gravity of paint is 0.8 .
50 . Compute the total weight of paint.

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SITUATION 9: A vat filled with paint is 9 m long. Its ends are in the form of trapezoid 3 m at the bottom and 5 m on the top. The vat is 4 m high and the specific gravity of paint is 0.8 . 50 . Compute the total weight of paint.

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SITUATION 9:
A vat filled with paint is 9 m long. Its ends are
in the form of trapezoid 3 m at the bottom and
5 m on the top. The vat is 4 m high and the
specific gravity of paint is 0.8 .
50 . Compute the total weight of paint.