Question

22 cm

d = 25cm

What is the surface area of the cone? Use 3.14 for pi

Answer 1

The formula for the surface area of a cone is given by:

Surface Area = π * r * (r + l)

where r is the radius of the base and l is the slant height.

Given that the diameter (d) is 25 cm, we can find the radius (r) by dividing the diameter by 2:

r = d/2 = 25 cm / 2 = 12.5 cm

Since the slant height (l) is not given, we need to use the Pythagorean theorem to find it. The height (h) can be found using the Pythagorean theorem in a right triangle with one leg as the height, the other leg as the radius, and the hypotenuse as the slant height:

h^2 + r^2 = l^2

Given that the height (h) is 22 cm, we can solve for the slant height (l):

l^2 = h^2 + r^2
l^2 = (22 cm)^2 + (12.5 cm)^2
l^2 = 484 cm^2 + 156.25 cm^2
l^2 = 640.25 cm^2
l ≈ 25.3 cm

Now we can substitute the values into the formula for the surface area of the cone:

Surface Area = π * r * (r + l)
Surface Area = 3.14 * 12.5 cm * (12.5 cm + 25.3 cm)
Surface Area = 3.14 * 12.5 cm * 37.8 cm
Surface Area ≈ 1,876.65 cm²

Therefore, the surface area of the cone is approximately 1,876.65 square cm.