Surface Area of Cones Practice

Question

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 and round to the nearest tenth, if necessary.

Answer 1

To find the surface area of a cone, we need to calculate the area of the curved lateral surface and the area of the base.

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 or the length of the side.

In this case, the radius of the base is 6 and the length of the side is 11. So, we have:

Lateral Surface Area = 3.14 * 6 * 11

Lateral Surface Area = 208.68 (rounded to the nearest hundredth)

The formula for the area of the base of a cone is given by:

Base Area = π*r^2

where r is the radius of the base.

In this case, the radius of the base is 6. So, we have:

Base Area = 3.14 * 6^2

Base Area = 3.14 * 36

Base Area = 113.04

To find the surface area of the cone, we add the lateral surface area and the base area:

Surface Area = Lateral Surface Area + Base Area

Surface Area = 208.68 + 113.04

Surface Area = 321.72 (rounded to the nearest hundredth)

Therefore, the surface area of the cone is approximately 321.72 square units.