It takes 13.5 mL to paint the surface of the circular sheet of radius 17 cm . How much paint is required to paint a similar circular sheet with double the radius ?

Answer

To find out how much paint is required to paint a circular sheet with double the radius, we can follow these steps:

### Step 1: Calculate the area of the original circular sheet.
The formula for the area \( A \) of a circle is given by:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.

For the original circular sheet with a radius of 17 cm:
\[ A_1 = \pi (17)^2 = \pi \times 289 \approx 908.1 \text{ cm}^2 \]

### Step 2: Calculate the radius of the new circular sheet.
The new circular sheet has double the radius of the original sheet:
\[ r_2 = 2 \times 17 = 34 \text{ cm} \]

### Step 3: Calculate the area of the new circular sheet.
Using the area formula again for the new radius:
\[ A_2 = \pi (34)^2 = \pi \times 1156 \approx 3637.9 \text{ cm}^2 \]

### Step 4: Determine the ratio of the areas.
The amount of paint required is proportional to the area of the circular sheet. The ratio of the areas of the new sheet to the original sheet is:
\[ \text{Ratio} = \frac{A_2}{A_1} = \frac{3637.9}{908.1} \approx 4 \]

### Step 5: Calculate the amount of paint required for the new sheet.
Since it takes 13.5 mL of paint to cover the original sheet, the amount of paint required for the new sheet is:
\[ \text{Paint required} = 13.5 \text{ mL} \times 4 = 54 \text{ mL} \]

### Final Answer:
The amount of paint required to paint the similar circular sheet with double the radius is **54 mL**.

---