Use the image to answer the question.
a cone with d = 25 and 22 cm
What is the surface area of the cone? Use 3.14 for pi and round to the nearest tenth, if necessary.
To find the surface area of the cone, we need to calculate the lateral surface area and the base area, and then add them together.
The formula for the lateral surface area of a cone is given by:
Lateral Surface Area = π × r × l
where r is the radius of the base and l is the slant height of the cone.
To find the radius of the base, we divide the diameter by 2:
r = d/2 = 25/2 = 12.5 cm
From the image, we can see that the slant height (l) is 22 cm.
Now, we can substitute these values into the formula:
Lateral Surface Area = 3.14 × 12.5 × 22 = 868.5 cm²
Next, we need to calculate the base area of the cone. The formula for the base area is given by:
Base Area = π × r²
Substituting our previously calculated radius:
Base Area = 3.14 × (12.5)² = 3.14 × 156.25 = 490.875 cm²
Finally, we 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 + 490.875
= 1359.375 cm²
Rounding to the nearest tenth, the surface area of the cone is 1359.4 cm².