8.5 Surface Area of Cones

Front

What is surface area?

Back

The sum of all the areas of all the shapes that cover the object.

Front

What is the formula for the surface area of a cone?

Back

Surface Area = πr(r + l), where r is the radius and l is the slant height.

Front

If a cone has a radius of 3 inches and a slant height of 4 inches, what is its surface area?

Back

Surface Area = π(3)(3 + 4) = π(3)(7) = 21π ≈ 65.97 in².

Front

What does 'slant height' refer to in a cone?

Back

The distance from the base of the cone to the apex along the side of the cone.

Front

How do you find the radius of a cone if you know the surface area and slant height?

Back

Rearrange the surface area formula: r = (Surface Area / (π(l + r))).

Front

What is the surface area of a cone with a radius of 5 cm and a slant height of 12 cm?

Back

Surface Area = π(5)(5 + 12) = π(5)(17) = 85π ≈ 267.35 cm².

Front

What is the relationship between the radius and the height of a cone?

Back

The height can be found using the Pythagorean theorem: h = √(l² - r²), where l is the slant height.

Front

If the radius of a cone doubles, how does the surface area change?

Back

The surface area increases by a factor of 4, since surface area is proportional to the square of the radius.

Front

What is the surface area of a cone with a radius of 2 m and a slant height of 3 m?

Back

Surface Area = π(2)(2 + 3) = π(2)(5) = 10π ≈ 31.42 m².

Front

What is the difference between the lateral surface area and the total surface area of a cone?

Back

Lateral surface area is the area of the cone's side, while total surface area includes the base area.