In the field of Mohanbhai, wheat is collected to form 10 conical heaps. The diameter of each heap is 140 cm and the height of each heap is 60 cm. All the wheat is stored in cylinders with radius 20 cm and 50 cm height. Find the number of cylinders required.

Answer

To solve the problem of how many cylindrical containers are needed to store the wheat collected in conical heaps, we will follow these steps:

### Step 1: Calculate the Volume of One Conical Heap
The formula for the volume \( V \) of a cone is given by:

\[ V = \frac{1}{3} \pi r^2 h \]

Where:
- \( r \) is the radius of the base of the cone
- \( h \) is the height of the cone

Given:
- Diameter of the heap = 140 cm, so the radius \( r = \frac{140}{2} = 70 \) cm
- Height \( h = 60 \) cm

Substituting these values into the formula:

\[ V = \frac{1}{3} \pi (70)^2 (60) \]

Calculating \( (70)^2 \):

\[ (70)^2 = 4900 \]

Now substituting this back into the volume formula:

\[ V = \frac{1}{3} \pi (4900) (60) = \frac{1}{3} \pi (294000) \]

So, the volume of one conical heap is:

\[ V = 98000 \pi \text{ cm}^3 \]

### Step 2: Calculate the Total Volume of 10 Conical Heaps
Since there are 10 conical heaps, the total volume \( V_{total} \) is:

\[ V_{total} = 10 \times 98000 \pi = 980000 \pi \text{ cm}^3 \]

### Step 3: Calculate the Volume of One Cylindrical Container
The formula for the volume \( V \) of a cylinder is given by:

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

Given:
- Radius \( r = 20 \) cm
- Height \( h = 50 \) cm

Substituting these values into the formula:

\[ V = \pi (20)^2 (50) \]

Calculating \( (20)^2 \):

\[ (20)^2 = 400 \]

Now substituting this back into the volume formula:

\[ V = \pi (400) (50) = 20000 \pi \text{ cm}^3 \]

### Step 4: Calculate the Number of Cylinders Required
To find the number of cylinders required, we divide the total volume of wheat by the volume of one cylinder:

\[ \text{Number of cylinders} = \frac{V_{total}}{V_{cylinder}} = \frac{980000 \pi}{20000 \pi} \]

The \( \pi \) cancels out:

\[ \text{Number of cylinders} = \frac{980000}{20000} = 49 \]

### Final Answer
The number of cylindrical containers required is **49**.

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