60 discs each of diameter 21 cm and thickness cm are stacked one above the other to form rightcircular cylinder. What is its volume in `m^3 " If " pi = 22/7` ?

Options

A. `4.25 xx 10^(-2)`
B. `8.05 xx 10^(-3)`
C. `7.62 xx 10^(-2)`
D. `6.93 xx 10^(-3)`

Answer

To find the volume of the right circular cylinder formed by stacking 60 discs, we can follow these steps:

### Step 1: Calculate the radius of the disc
The diameter of each disc is given as 21 cm. The radius (r) is half of the diameter.

\[ r = \frac{21 \text{ cm}}{2} = 10.5 \text{ cm} \]

**Hint:** Remember that the radius is always half of the diameter.

### Step 2: Calculate the height of the cylinder
The thickness of each disc is given as 1.3 cm. When 60 discs are stacked, the total height (h) of the cylinder is the thickness of one disc multiplied by the number of discs.

\[ h = 60 \times 1.3 \text{ cm} = 78 \text{ cm} \]

**Hint:** To find the height of a stack, multiply the thickness of one item by the number of items.

### Step 3: Calculate the volume of the cylinder
The volume (V) of a cylinder is given by the formula:

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

Substituting the values we have:

\[ V = \frac{22}{7} \times (10.5 \text{ cm})^2 \times 78 \text{ cm} \]

Calculating \( (10.5 \text{ cm})^2 \):

\[ (10.5)^2 = 110.25 \text{ cm}^2 \]

Now substituting this back into the volume formula:

\[ V = \frac{22}{7} \times 110.25 \text{ cm}^2 \times 78 \text{ cm} \]

### Step 4: Simplify the volume calculation
Calculating the volume step by step:

\[ V = \frac{22 \times 110.25 \times 78}{7} \]

Calculating \( 22 \times 110.25 = 2425.5 \):

\[ V = \frac{2425.5 \times 78}{7} \]

Calculating \( 2425.5 \times 78 = 189969 \):

\[ V = \frac{189969}{7} = 27139.857 \text{ cm}^3 \]

### Step 5: Convert the volume to cubic meters
To convert cubic centimeters to cubic meters, we divide by \( 1,000,000 \) (since \( 1 \text{ m}^3 = 1,000,000 \text{ cm}^3 \)):

\[ V = \frac{27139.857 \text{ cm}^3}{1000000} = 0.027139857 \text{ m}^3 \]

### Final Step: Round the answer
Rounding to three significant figures gives:

\[ V \approx 0.0271 \text{ m}^3 \]

### Conclusion
The volume of the cylinder formed by stacking the discs is approximately \( 0.0271 \text{ m}^3 \).