Which is false? Write the correct answer. For a right circular cylinder of base radius=7cm and height =14cm

Options

A. curved surface area=`616cm^(2)`
B. Total surface area`=924cm^(2)`
C. Volume`=2156cm^(3)`
D. Totl area of the end face`=154cm^(2)`

Answer

To solve the problem, we need to determine which statement about the right circular cylinder with a base radius of 7 cm and a height of 14 cm is false. We will calculate the curved surface area, total surface area, and volume of the cylinder, and then check the options provided.

### Step-by-Step Solution:

1. **Calculate the Curved Surface Area (CSA)**:
The formula for the curved surface area of a right circular cylinder is given by:
\[ \text{CSA} = 2 \pi r h \]
Where:
- \( r = 7 \, \text{cm} \)
- \( h = 14 \, \text{cm} \)

Substituting the values:
\[ \text{CSA} = 2 \times \frac{22}{7} \times 7 \times 14 \]
Simplifying:
\[ \text{CSA} = 2 \times 22 \times 14 = 616 \, \text{cm}^2 \]

2. **Calculate the Total Surface Area (TSA)**:
The formula for the total surface area of a right circular cylinder is:
\[ \text{TSA} = 2 \pi r h + 2 \pi r^2 \]
We already calculated \( 2 \pi r h = 616 \, \text{cm}^2 \). Now, we need to calculate \( 2 \pi r^2 \):
\[ 2 \pi r^2 = 2 \times \frac{22}{7} \times (7)^2 = 2 \times \frac{22}{7} \times 49 \]
Simplifying:
\[ 2 \pi r^2 = 2 \times 22 \times 7 = 308 \, \text{cm}^2 \]
Now, adding both areas:
\[ \text{TSA} = 616 + 308 = 924 \, \text{cm}^2 \]

3. **Calculate the Volume (V)**:
The formula for the volume of a right circular cylinder is:
\[ V = \pi r^2 h \]
Substituting the values:
\[ V = \frac{22}{7} \times (7)^2 \times 14 \]
Simplifying:
\[ V = \frac{22}{7} \times 49 \times 14 = 22 \times 14 = 308 \times 7 = 2156 \, \text{cm}^3 \]

4. **Calculate the Area of the End Face**:
The area of one end face of the cylinder is given by:
\[ \text{Area of one end face} = \pi r^2 \]
Substituting the values:
\[ \text{Area of one end face} = \frac{22}{7} \times (7)^2 = \frac{22}{7} \times 49 = 154 \, \text{cm}^2 \]
Therefore, the total area of both end faces is:
\[ \text{Total area of end faces} = 2 \times 154 = 308 \, \text{cm}^2 \]

### Conclusion:
After calculating all the values, we can summarize:
- Curved Surface Area: \( 616 \, \text{cm}^2 \) (Correct)
- Total Surface Area: \( 924 \, \text{cm}^2 \) (Correct)
- Volume: \( 2156 \, \text{cm}^3 \) (Correct)
- Total Area of End Faces: \( 308 \, \text{cm}^2 \) (Correct)

If any option states that the total area of the end face is \( 154 \, \text{cm}^2 \), that would be false since the total area of both end faces is \( 308 \, \text{cm}^2 \).