A heap of rice is in the form of a cone of diameter 9 m and height 3.5 m. Find the volume of rice. How much canvas cloth is required to just cover the heap?

Answer

To solve the problem, we will follow these steps:

### Step 1: Find the volume of the cone (heap of rice).
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 cone = 9 m, therefore the radius \( r = \frac{9}{2} = 4.5 \) m.
- Height \( h = 3.5 \) m.

Now, substituting the values into the formula:

\[ V = \frac{1}{3} \pi (4.5)^2 (3.5) \]

Calculating \( (4.5)^2 \):

\[ (4.5)^2 = 20.25 \]

Now substituting back:

\[ V = \frac{1}{3} \pi (20.25)(3.5) \]

Calculating \( 20.25 \times 3.5 \):

\[ 20.25 \times 3.5 = 70.875 \]

Now substituting this value:

\[ V = \frac{1}{3} \pi (70.875) \]

Using \( \pi \approx 3.14 \):

\[ V \approx \frac{1}{3} \times 3.14 \times 70.875 \]

Calculating \( \frac{1}{3} \times 3.14 \):

\[ \frac{3.14}{3} \approx 1.047 \]

Now calculating:

\[ V \approx 1.047 \times 70.875 \approx 74.25 \, \text{m}^3 \]

### Step 2: Find the curved surface area (CSA) of the cone.
The formula for the curved surface area \( A \) of a cone is given by:

\[ A = \pi r l \]

Where \( l \) is the slant height of the cone. To find \( l \), we use the Pythagorean theorem:

\[ l = \sqrt{r^2 + h^2} \]

Calculating \( l \):

\[ l = \sqrt{(4.5)^2 + (3.5)^2} \]

Calculating \( (4.5)^2 \) and \( (3.5)^2 \):

\[ (4.5)^2 = 20.25, \quad (3.5)^2 = 12.25 \]

Now substituting back:

\[ l = \sqrt{20.25 + 12.25} = \sqrt{32.5} \]

Calculating \( \sqrt{32.5} \):

\[ l \approx 5.7 \, \text{m} \]

Now substituting \( r \) and \( l \) into the CSA formula:

\[ A = \pi (4.5)(5.7) \]

Using \( \pi \approx 3.14 \):

\[ A \approx 3.14 \times 4.5 \times 5.7 \]

Calculating \( 4.5 \times 5.7 \):

\[ 4.5 \times 5.7 = 25.65 \]

Now substituting back:

\[ A \approx 3.14 \times 25.65 \approx 80.61 \, \text{m}^2 \]

### Final Answers:
- Volume of rice = \( 74.25 \, \text{m}^3 \)
- Canvas cloth required = \( 80.61 \, \text{m}^2 \)