A cylindrical grain silo has a height of 12 inches and a radius of 4 inches. The silo is filled with grain up to 

75% of its total capacity. If 1 cubic yd of grain weighs 2 kilograms, what is the total weight of the grain inside 

the silo?

To solve this problem, we need to calculate the volume of the cylindrical silo, then find 75% of that volume, convert it to cubic yards, and finally determine the weight of the grain inside.

### Step 1: Calculate the volume of the cylinder
The formula for the volume \( V \) of a cylinder is given by:

\[
V = \pi r^2 h
\]

Where:
- \( r \) is the radius of the base (4 inches)
- \( h \) is the height of the silo (12 inches)
- \( \pi \approx 3.1416 \)

Substitute the values into the formula:

\[
V = \pi (4)^2 (12) = \pi (16)(12) = 192\pi \, \text{cubic inches}
\]

So, the total volume is:

\[
V \approx 192 \times 3.1416 = 603.19 \, \text{cubic inches}
\]

### Step 2: Find 75% of the total volume
Since the silo is filled to 75% of its capacity, we calculate:

\[
\text{Filled Volume} = 0.75 \times 603.19 \approx 452.39 \, \text{cubic inches}
\]

### Step 3: Convert cubic inches to cubic yards
There are 46,656 cubic inches in a cubic yard (since \( 36 \times 36 \times 36 = 46,656 \)).

\[
\text{Filled Volume in Cubic Yards} = \frac{452.39}{46,656} \approx 0.0097 \, \text{cubic yards}
\]

### Step 4: Calculate the weight of the grain
It is given that 1 cubic yard of grain weighs 2 kilograms. Therefore, the weight of the grain is:

\[
\text{Weight} = 0.0097 \times 2 \approx 0.0194 \, \text{kilograms}
\]

### Final Answer:
The total weight of the grain inside the silo is approximately **0.0194 kilograms**.

---

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How would the weight change if the silo were filled to 100%?
2. How does changing the radius of the silo affect the total weight?
3. What would happen to the weight if the silo's height were doubled?
4. How much grain would be needed to fill another silo with a radius of 6 inches and the same height?
5. How can you convert between other units of volume, such as gallons or liters?

**Tip:** Always double-check your unit conversions when solving problems involving different measurement systems!

A cylindrical grain silo has a height of 12 inches and a radius of 4 inches. The silo is filled with grain up to 75% of its total capacity. If 1 cubic yard of grain weighs 2 kilograms, what is the total weight of the grain inside the silo?

Find the total weight of grain in a cylindrical silo with a radius of 4 inches and height of 12 inches, filled to 75% capacity. Learn step-by-step how to calculate the volume of the cylinder, convert cubic inches to cubic yards, and determine the weight based on the provided density. Suitable for Grades 9-10.

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