Kamala has three cylindrical containers, each with radius 20 cm that she wants to fill with grain. If her bag of grain contains 100 kg of grain, and she fills all three containers to a height of 70 cm. how much grain will be left in the bag. if 1kg grain occupies `3000 cm^3` space ?

Options

A. 88kg
B. 50kg
C. 58kg
D. 12kg

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the volume of one cylindrical container
The formula for the volume \( V \) of a cylinder is given by:
\[ V = \pi r^2 h \]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.

Given:
- Radius \( r = 20 \) cm,
- Height \( h = 70 \) cm,
- Using \( \pi \approx \frac{22}{7} \).

Substituting the values into the formula:
\[ V = \frac{22}{7} \times (20)^2 \times 70 \]
Calculating \( (20)^2 = 400 \):
\[ V = \frac{22}{7} \times 400 \times 70 \]
Calculating \( 400 \times 70 = 28000 \):
\[ V = \frac{22}{7} \times 28000 \]
Calculating \( \frac{22 \times 28000}{7} = 22 \times 4000 = 88000 \) cm³.

### Step 2: Calculate the total volume of three containers
Since there are three identical containers, the total volume \( V_{total} \) is:
\[ V_{total} = 3 \times V = 3 \times 88000 = 264000 \text{ cm}^3. \]

### Step 3: Calculate the amount of grain in kg that can fill the total volume
We know that 1 kg of grain occupies 3000 cm³. Therefore, the amount of grain in kg that can fill the total volume is:
\[ \text{Grain in kg} = \frac{V_{total}}{3000} = \frac{264000}{3000}. \]
Calculating this gives:
\[ \text{Grain in kg} = 88 \text{ kg}. \]

### Step 4: Calculate the amount of grain left in the bag
Kamala started with 100 kg of grain. After filling the containers, the amount of grain left is:
\[ \text{Grain left} = 100 \text{ kg} - 88 \text{ kg} = 12 \text{ kg}. \]

### Final Answer
The amount of grain left in the bag is **12 kg**.

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