Question
22 cm d 25 cm What is the surface area of the cone? Use 3 14 for ( point )
Answers
GPT 3.5
The surface area of a cone can be calculated using the formula:
Surface Area = π * r * (r + l)
where r is the radius of the base and l is the slant height.
Given that the diameter of the base (d) is 22 cm, we can find the radius (r) by dividing it by 2:
r = d/2 = 22 cm / 2 = 11 cm
The slant height (l) can be found using the Pythagorean theorem. In a right triangle formed by the radius (r), slant height (l), and height (h), we can apply the following equation:
r^2 + h^2 = l^2
Given that the height of the cone (h) is 25 cm, we can solve for the slant height (l):
l^2 = r^2 + h^2
l^2 = (11 cm)^2 + (25 cm)^2
l^2 = 121 cm^2 + 625 cm^2
l^2 = 746 cm^2
l = √(746 cm^2)
l ≈ 27.31 cm
Now we can calculate the surface area using the formula:
Surface Area = π * r * (r + l)
Surface Area = 3.14 * 11 cm * (11 cm + 27.31 cm)
Surface Area = 3.14 * 11 cm * 38.31 cm
Surface Area ≈ 1,321.774 cm^2
Therefore, the surface area of the cone is approximately 1,321.774 cm².
Surface Area = π * r * (r + l)
where r is the radius of the base and l is the slant height.
Given that the diameter of the base (d) is 22 cm, we can find the radius (r) by dividing it by 2:
r = d/2 = 22 cm / 2 = 11 cm
The slant height (l) can be found using the Pythagorean theorem. In a right triangle formed by the radius (r), slant height (l), and height (h), we can apply the following equation:
r^2 + h^2 = l^2
Given that the height of the cone (h) is 25 cm, we can solve for the slant height (l):
l^2 = r^2 + h^2
l^2 = (11 cm)^2 + (25 cm)^2
l^2 = 121 cm^2 + 625 cm^2
l^2 = 746 cm^2
l = √(746 cm^2)
l ≈ 27.31 cm
Now we can calculate the surface area using the formula:
Surface Area = π * r * (r + l)
Surface Area = 3.14 * 11 cm * (11 cm + 27.31 cm)
Surface Area = 3.14 * 11 cm * 38.31 cm
Surface Area ≈ 1,321.774 cm^2
Therefore, the surface area of the cone is approximately 1,321.774 cm².