Surface Area of Cones Practice
Math 8 Q2 (Pre-Algebra) / Cones, Cylinders, & Spheres
Use the image to answer the question.
A cone shows a radius of 6 and hypotenuse or side as 11.
what is the surface area of the cone? use 3.14 for pi
To find the surface area of a cone, you need to add the area of the base to the lateral surface area.
The formula for the base area of a cone is A = πr^2, where A is the base area and r is the radius.
Given that the radius is 6, we can calculate the base area:
A_base = π(6)^2 = 36π
The formula for the lateral surface area of a cone is A_lateral = πrs, where A_lateral is the lateral surface area, r is the radius, and s is the slant height.
We can calculate the slant height using the Pythagorean theorem:
s = √(h^2 + r^2), where h is the height (or the vertical distance from the apex to the base) and r is the radius.
Given that the hypotenuse or side is 11, and the radius is 6, we can calculate the height:
s = √(h^2 + 6^2)
11 = √(h^2 + 36)
11^2 = h^2 + 36
121 = h^2 + 36
h^2 = 121 - 36
h^2 = 85
h ≈ √85 (approximately)
Now that we have the slant height, we can calculate the lateral surface area:
A_lateral = π(6)(√85) (approximately)
Finally, we can find the surface area of the cone by adding the base area and the lateral surface area:
A_total = A_base + A_lateral
A_total = 36π + π(6)(√85) (approximately)
Now you can calculate the surface area using 3.14 as the approximation for π.