4. A core sample of earth is cylindrical. The length of the core is 300 mm . Its diameter is 150 mm . Calculate the volume of earth in cubic millimetres and cubic centimetres.

Question

UpStudy AI · Accepted Answer

To calculate the volume of the cylindrical core sample of earth, we'll use the formula for the volume of a cylinder:

$$ V = \pi r^2 h $$

where:
- $$ V $$ is the volume,
- $$ r $$ is the radius of the cylinder,
- $$ h $$ is the height (length) of the cylinder,
- $$ \pi $$ is approximately 3.1416.

### Given:
- **Diameter of the core (d)** = 150 mm
- **Radius (r)** = $$ \frac{d}{2} = \frac{150 \text{ mm}}{2} = 75 \text{ mm} $$
- **Height (h)** = 300 mm

### Step-by-Step Calculation:

1. **Calculate the volume in cubic millimeters (mm³):**

$$
   V = \pi r^2 h = \pi \times (75 \text{ mm})^2 \times 300 \text{ mm}
   $$
   
   $$
   V = \pi \times 5625 \text{ mm}^2 \times 300 \text{ mm} = 1,687,500 \pi \text{ mm}^3
   $$
   
   $$
   V \approx 1,687,500 \times 3.1416 \approx 5,301,450 \text{ mm}^3
   $$

2. **Convert cubic millimeters to cubic centimeters (cm³):**

Since $$ 1 \text{ cm}^3 = 1,000 \text{ mm}^3 $$,
   
   $$
   V = \frac{5,301,450 \text{ mm}^3}{1,000} \approx 5,301.45 \text{ cm}^3
   $$

### **Final Answer:**

- **Volume of the core:**  
  - Approximately **5,301,450 mm³**  
  - Or, equivalently, **5,301.45 cm³**
The volume of the cylindrical core sample is approximately 5,301,450 mm³ or 5,301.45 cm³.

A core sample of earth is cylindrical.
The length of the core is 300 mm .
Its diameter is 150 mm .
Calculate the volume of earth in cubic millimetres
and cubic centimetres.

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