Question

What is the surface area of the cone diameter is 25 cm height is 22 cm use 3.14 for pi

Answer 1

To find the surface area of the cone, we need to calculate the lateral surface area plus the base area.

The lateral surface area of a cone can be calculated using the formula:
Lateral Surface Area = π * r * s, where r is the radius and s is the slant height.

Given that the diameter of the cone is 25 cm, we can calculate the radius by dividing it by 2:
Radius (r) = Diameter / 2 = 25 cm / 2 = 12.5 cm

To calculate the slant height (s), we can use the Pythagorean theorem:
s = √(r^2 + h^2)
where h is the height.

Plugging in the values:
s = √(12.5^2 + 22^2)
s ≈ √(156.25 + 484)
s ≈ √640.25
s ≈ 25.3 cm (rounded to one decimal place)

The lateral surface area is then:
Lateral Surface Area = π * r * s
Lateral Surface Area = 3.14 * 12.5 cm * 25.3 cm
Lateral Surface Area ≈ 994.525 cm² (rounded to three decimal places)

The base area of the cone is given by:
Base Area = π * r^2
Base Area = 3.14 * (12.5 cm)^2
Base Area ≈ 490.875 cm² (rounded to three decimal places)

Therefore, the total surface area of the cone is:
Total Surface Area = Lateral Surface Area + Base Area
Total Surface Area ≈ 994.525 cm² + 490.875 cm²
Total Surface Area ≈ 1485.4 cm² (rounded to one decimal place)