Given:
- Base area of the tent = 154 cm^2
- Covered surface area of the tent = 396 cm^2

To find:
- Radius and height of the conical tent

Formula:
- The formula for the base area of a cone is A = πr^2, where A is the base area and r is the radius.
- The formula for the surface area of a cone is SA = πr(r + l), where SA is the surface area, r is the radius, and l is the slant height.

Solution:

1. Calculating the radius:
Given that the base area of the tent is 154 cm^2, we can use the formula A = πr^2 to find the radius.
154 = πr^2

To solve for r, divide both sides of the equation by π:
154/π = r^2

Take the square root of both sides to find the radius:
√(154/π) = r

Therefore, the radius of the conical tent is √(154/π).

2. Calculating the slant height:
Given that the covered surface area of the tent is 396 cm^2, we can use the formula SA = πr(r + l) to find the slant height.
396 = πr(r + l)

Since we have already found the value of r, we can substitute it into the equation:
396 = π(√(154/π))(√(154/π) + l)

Simplify the equation:
396 = π(154/π + l)

Distribute π to both terms inside the parentheses:
396 = 154 + πl

Rearrange the equation to isolate l:
πl = 396 - 154
l = (396 - 154)/π

Therefore, the slant height of the conical tent is (396 - 154)/π.

3. Calculating the height:
To find the height of the conical tent, we can use the Pythagorean theorem.
The height, radius, and slant height form a right triangle.

Using the equation a^2 + b^2 = c^2, where a and b are the legs of the right triangle and c is the hypotenuse (slant height), we can substitute the known values:
h^2 + r^2 = l^2

Substitute the values of r and l:
h^2 + (√(154/π))^2 = [(396 - 154)/π]^2

Simplify the equation:
h^2 + 154/π = [(396 - 154)/π]^2

Multiply both sides by π:
πh^2 + 154 = (396 - 154)^2

Simplify the equation:
πh^2 + 154 = 242^2

Rearrange the equation to isolate h:
πh^2 = 242^2 - 154
h^2 = (242^2 - 154)/π
h = √[(242^2 - 154)/π]

Therefore, the height of the conical tent is √[(242^2 - 154)/π].

Conclusion:
The radius of the con