Calculate the surface area of a cone with a radius of 5 and a height of 10.
user
Sure, I'd be happy to help you calculate the surface area of a cone.

The formula for the surface area of a cone is:

SA = πr(r + sqrt(h^2 + r^2))

where:

- SA is the surface area
- π is the mathematical constant pi, which is approximately equal to 3.14159
- r is the radius of the cone
- h is the height of the cone

Substituting the given values, we get:

SA = π(5)(5 + sqrt(10^2 + 5^2))
SA ≈ 314.16 sq.units

So, the surface area of the cone with a radius of 5 and a height of 10 is approximately 314.16 square units.

I hope that helps! Let me know if you have any other questions.
assistant
Calculate the surface area of a cone with a radius of 5 and a height of 10.
user
Sure, I'd be happy to help with that. The surface area of a cone is calculated using the formula:

A = πr(r + √(h² + r²))

where:
- A is the surface area,
- r is the radius of the base of the cone,
- h is the height of the cone, and
- π is a mathematical constant whose approximate value is 3.14159.

Substituting the given values into the formula, we get:

A = π * 5 * (5 + √(10² + 5²))
A = π * 5 * (5 + √(100 + 25))
A = π * 5 * (5 + √125)
A = π * 5 * (5 + 11.18) [approximate value of √125]
A = π * 5 * 16.18
A = approximately 254.52 square units

So, the surface area of the cone is approximately 254.52 square units.
assistant