Read the given statements carefully and select the correct option
Statement - 1 : If the radii of two right circular cylinders are in the ration 1 : 2 and their height are in the ratio 4 : 3 then the ratio of their curved surface areas is 2 : 3
Statement - 2 : If each edge of a cube is doubled, then the surface area of the new cube will become three times

Options

A. Statement - 1 is false but Statement - 2 is true
B. Statement - 1 is true but Statement - 2 is false
C. Both Statement - 1 and Statement - 2 are true
D. Both Statement - 1 and Statement - 2 are false

Explanation

To solve the problem, we will analyze both statements one by one.

### Statement 1:
We have two right circular cylinders with the following properties:
- The ratio of their radii \( r_1 : r_2 = 1 : 2 \)
- The ratio of their heights \( h_1 : h_2 = 4 : 3 \)

**Step 1: Write the formulas for the curved surface area (CSA) of a cylinder.**
The formula for the curved surface area of a cylinder is given by:
\[ \text{CSA} = 2\pi rh \]

**Step 2: Calculate the CSA for both cylinders.**
Let’s denote:
- For Cylinder 1: \( r_1 = r \) and \( h_1 = 4h \) (since the ratio of heights is 4:3)
- For Cylinder 2: \( r_2 = 2r \) and \( h_2 = 3h \)

Now, we can calculate the CSA for both cylinders:

- CSA of Cylinder 1:
\[ \text{CSA}_1 = 2\pi r h_1 = 2\pi r (4h) = 8\pi rh \]

- CSA of Cylinder 2:
\[ \text{CSA}_2 = 2\pi r_2 h_2 = 2\pi (2r) (3h) = 12\pi rh \]

**Step 3: Find the ratio of the curved surface areas.**
Now, we find the ratio of the curved surface areas:
\[ \frac{\text{CSA}_1}{\text{CSA}_2} = \frac{8\pi rh}{12\pi rh} = \frac{8}{12} = \frac{2}{3} \]

### Conclusion for Statement 1:
The ratio of the curved surface areas of the two cylinders is indeed \( 2 : 3 \). Thus, Statement 1 is **True**.

---

### Statement 2:
The statement claims that if each edge of a cube is doubled, then the surface area of the new cube will become three times the original surface area.

**Step 1: Write the formula for the surface area of a cube.**
The surface area \( A \) of a cube with edge length \( a \) is given by:
\[ A = 6a^2 \]

**Step 2: Calculate the surface area of the new cube after doubling the edge length.**
If the edge length is doubled, the new edge length becomes \( 2a \). The surface area of the new cube is:
\[ A' = 6(2a)^2 = 6 \cdot 4a^2 = 24a^2 \]

**Step 3: Compare the new surface area with the original surface area.**
The original surface area was \( 6a^2 \). Now, we find the ratio:
\[ \frac{A'}{A} = \frac{24a^2}{6a^2} = 4 \]

### Conclusion for Statement 2:
The surface area of the new cube is four times the original surface area, not three times. Thus, Statement 2 is **False**.

---

### Final Conclusion:
- Statement 1 is **True**.
- Statement 2 is **False**.