what is the surface area of the cone? use 3.14 for pi.
slant height = 22 cm
diameter = 25 cm
To find the surface area of a cone, you need to calculate both the lateral surface area (the curved part) and the base area.
First, let's find the radius of the cone:
The diameter is given as 25 cm, so the radius is half of that:
radius = diameter / 2 = 25 cm / 2 = 12.5 cm
Now, let's find the lateral surface area:
Lateral surface area = π × radius × slant height
= 3.14 × 12.5 cm × 22 cm
= 868.5 cm²
Next, let's find the base area:
The base area of a cone is given by: π × radius²
= 3.14 × (12.5 cm)²
= 3.14 × 156.25 cm²
= 490.625 cm²
Finally, add the lateral surface area and the base area to get the total surface area of the cone:
Total surface area = Lateral surface area + Base area
= 868.5 cm² + 490.625 cm²
= 1359.125 cm²
Therefore, the surface area of the cone is approximately 1359.125 cm².
A spyglass in the shape of a cone has a slant height of 18 centimeters and a radius of 6 centimeters. What is the surface area of the spyglass? Use 3.14 for pi
To find the surface area of the spyglass, we need to calculate both the lateral surface area and the base area.
First, let's find the lateral surface area:
Lateral surface area = π × radius × slant height
= 3.14 × 6 cm × 18 cm
= 339.12 cm²
Next, let's find the base area:
The base area of a cone is given by: π × radius²
= 3.14 × (6 cm)²
= 113.04 cm²
Finally, calculate the total surface area by adding the lateral surface area and the base area:
Total surface area = Lateral surface area + Base area
= 339.12 cm² + 113.04 cm²
= 452.16 cm²
Therefore, the surface area of the spyglass is approximately 452.16 cm².
To find the surface area of a cone, we need to calculate the lateral surface area and the base area, and then sum them up.
First, let's find the slant height of the cone using Pythagoras theorem. The slant height (l) of a cone is the hypotenuse of a right triangle, with the height (h) as one leg and the radius (r) as the other leg.
Given: Diameter = 25 cm
Therefore, Radius (r) = diameter / 2 = 25 cm / 2 = 12.5 cm
Slant height (l) = 22 cm
Using Pythagoras theorem:
l^2 = r^2 + h^2
Substituting the given values:
22^2 = 12.5^2 + h^2
484 = 156.25 + h^2
h^2 = 484 - 156.25
h^2 = 327.75
h = sqrt(327.75)
h ≈ 18.1 cm (rounded to one decimal place)
Now that we have the height (h) and the slant height (l), we can proceed to find the lateral surface area and base area.
Lateral surface area (A_l) of a cone is given by the formula:
A_l = π * r * l
Substituting the given values:
A_l = 3.14 * 12.5 cm * 22 cm
A_l ≈ 865.7 cm^2 (rounded to one decimal place)
The base area (A_b) of a cone is given by the formula:
A_b = π * r^2
Substituting the given values:
A_b = 3.14 * (12.5 cm)^2
A_b ≈ 490.875 cm^2 (rounded to three decimal places)
Now, we can find the total surface area (A) of the cone by summing up the lateral surface area and the base area:
A = A_l + A_b
A ≈ 865.7 cm^2 + 490.875 cm^2
A ≈ 1356.575 cm^2 (rounded to three decimal places)
Therefore, the surface area of the cone is approximately 1356.575 cm^2.