The amount of concrete required to build a cylindrical pillar whose base has a perimeter of 8.8 m and whose curved surface area is `17.6 m^(2)` :

Options

A. `12.32 m^(3) `
B. `12.23 m^(3) `
C. `9.235 m^(3) `
D. `8.88 m^(3) `

Answer

To find the amount of concrete required to build a cylindrical pillar, we need to calculate the volume of the cylinder using the given perimeter of the base and the curved surface area. Here’s a step-by-step solution:

### Step 1: Find the radius of the base
The perimeter (circumference) of the base of the cylinder is given as 8.8 m. The formula for the perimeter of a circle is:
\[ \text{Perimeter} = 2\pi r \]
Setting this equal to the given perimeter:
\[ 2\pi r = 8.8 \]
Using \(\pi \approx \frac{22}{7}\):
\[ 2 \times \frac{22}{7} \times r = 8.8 \]
Now, simplify:
\[ \frac{44}{7} r = 8.8 \]
To isolate \(r\), multiply both sides by \(\frac{7}{44}\):
\[ r = 8.8 \times \frac{7}{44} \]
Calculating this gives:
\[ r = \frac{8.8 \times 7}{44} = \frac{61.6}{44} = 1.4 \text{ m} \]

### Step 2: Find the height of the cylinder
The curved surface area (CSA) of the cylinder is given as 17.6 m². The formula for the curved surface area is:
\[ \text{CSA} = 2\pi rh \]
Setting this equal to the given CSA:
\[ 2\pi rh = 17.6 \]
Substituting the value of \(\pi\) and \(r\):
\[ 2 \times \frac{22}{7} \times 1.4 \times h = 17.6 \]
Simplifying:
\[ \frac{44}{7} \times 1.4 \times h = 17.6 \]
Calculating \(44 \times 1.4\):
\[ \frac{61.6}{7} h = 17.6 \]
Now, multiply both sides by 7:
\[ 61.6h = 123.2 \]
To find \(h\), divide both sides by 61.6:
\[ h = \frac{123.2}{61.6} = 2 \text{ m} \]

### Step 3: Calculate the volume of the cylinder
The volume \(V\) of the cylinder is given by the formula:
\[ V = \pi r^2 h \]
Substituting the values of \(\pi\), \(r\), and \(h\):
\[ V = \frac{22}{7} \times (1.4)^2 \times 2 \]
Calculating \(1.4^2\):
\[ 1.4^2 = 1.96 \]
Now substituting this value:
\[ V = \frac{22}{7} \times 1.96 \times 2 \]
Calculating the volume:
\[ V = \frac{22 \times 1.96 \times 2}{7} = \frac{86.56}{7} = 12.36 \text{ m}^3 \]

### Conclusion
The amount of concrete required to build the cylindrical pillar is approximately **12.36 m³**.

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