A cylindrical tank 3 m in diameter, 5m high is full of oil. If the specific gravity of oil is 0.80, what is the total mass and weight of oil in the tank?

To solve this problem, we need to find the volume of the oil in the cylindrical tank, then use the specific gravity to calculate its density and determine both the mass and weight of the oil.

### Given Data:
- Diameter of the tank, \( d = 3 \, \text{m} \)
- Height of the tank, \( h = 5 \, \text{m} \)
- Specific gravity of oil, \( SG = 0.80 \)

#### 1. Calculate the Volume of the Tank:
The volume \( V \) of a cylinder is given by:
\[
V = \pi r^2 h
\]
where:
- \( r \) is the radius of the tank, which is half the diameter, so \( r = \frac{3}{2} = 1.5 \, \text{m} \).
- \( h = 5 \, \text{m} \).

Plugging in the values:
\[
V = \pi (1.5)^2 \times 5
\]
\[
V = \pi \times 2.25 \times 5
\]
\[
V = 11.25\pi \approx 35.34 \, \text{m}^3
\]

#### 2. Calculate the Density of the Oil:
The specific gravity (SG) relates the density of the oil to the density of water. The density of water is approximately \( 1000 \, \text{kg/m}^3 \), so:
\[
\text{Density of oil} = SG \times \text{Density of water}
\]
\[
\text{Density of oil} = 0.80 \times 1000
\]
\[
\text{Density of oil} = 800 \, \text{kg/m}^3
\]

#### 3. Calculate the Mass of the Oil:
The mass \( m \) of the oil is given by:
\[
m = \text{Density} \times \text{Volume}
\]
\[
m = 800 \times 35.34
\]
\[
m \approx 28272 \, \text{kg}
\]

#### 4. Calculate the Weight of the Oil:
The weight \( W \) is given by:
\[
W = m \times g
\]
where \( g \) is the acceleration due to gravity, approximately \( 9.81 \, \text{m/s}^2 \):
\[
W = 28272 \times 9.81


Learn how to calculate the total mass and weight of oil in a cylindrical tank with a 3-meter diameter and 5-meter height. Using specific gravity, density, and volume formulas, this example provides a comprehensive solution ideal for high school students studying geometry and physics concepts.

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