Find the surface area of a cone if the diameter of its base is 13.5 feet, and it has a slant height of 16.8 feet. Round to the nearest tenth.
a = pi r^2 + pi r s = pi* 13.5/2 (13.5/2 + 16.8) = 158 77/80 pi
To find the surface area of a cone, we need to find the lateral surface area first. The lateral surface area is given by the formula:
Lateral Surface Area = π * r * l
Where:
- π is a constant approximately equal to 3.14159
- r is the radius of the base of the cone
- l is the slant height
The radius (r) of the base of the cone can be found by dividing the diameter (d) by 2:
r = d/2
In this case, the diameter (d) of the base is 13.5 feet, so the radius (r) is:
r = 13.5 / 2 = 6.75 feet
Now, we can substitute the values into the formula:
Lateral Surface Area = π * 6.75 * 16.8
Lateral Surface Area (LSA) ≈ 3.14159 * 6.75 * 16.8 ≈ 357.7116 square feet
The total surface area of the cone includes the base as well. The base is a circle with radius r, so its area is π * r^2. We can find that:
Base Area = π * 6.75^2 ≈ 143.1027 square feet
To find the total surface area, we add the lateral surface area and the base area:
Total Surface Area = Lateral Surface Area + Base Area
Total Surface Area ≈ 357.7116 + 143.1027
Total Surface Area ≈ 500.8143
Therefore, the surface area of the cone is approximately 500.8 square feet (rounded to the nearest tenth).
To find the surface area of a cone, we need to calculate the sum of the lateral surface area and the base area.
Step 1: Find the radius of the base
The diameter (d) is given as 13.5 feet. The radius (r) can be found by dividing the diameter by 2:
r = d/2 = 13.5/2 = 6.75 feet
Step 2: Calculate the slant height (l)
The slant height (l) is given as 16.8 feet.
Step 3: Calculate the lateral surface area
The lateral surface area (A) of a cone can be calculated using the formula: A = π * r * l
Substituting the values:
A = π * 6.75 feet * 16.8 feet ≈ 341.7 square feet
Step 4: Calculate the base area
The base area (B) of a cone can be calculated using the formula: B = π * r^2
Substituting the values:
B = π * (6.75 feet)^2 ≈ 143.04 square feet
Step 5: Find the total surface area
The total surface area (T) of a cone is the sum of the lateral surface area and the base area:
T = A + B ≈ 341.7 square feet + 143.04 square feet ≈ 484.74 square feet
Therefore, the surface area of the cone is approximately 484.7 square feet (rounded to the nearest tenth).