Lateral Area and Surface Area of cones

Front

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

Back

The lateral area (LA) of a cone is given by the formula: LA = πrl, where r is the radius of the base and l is the slant height.

Front

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

Back

The surface area (SA) of a cone is given by the formula: SA = πr(r + l), where r is the radius of the base and l is the slant height.

Front

Define 'slant height' in the context of a cone.

Back

Slant height (l) is the distance from the top of the cone to the edge of the base along the side of the cone.

Front

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

Back

The radius (r) is the distance from the center of the base to its edge, while the height (h) is the perpendicular distance from the base to the apex of the cone.

Front

How do you calculate the lateral area of a cone with a radius of 5 cm and a slant height of 10 cm?

Back

Using the formula LA = πrl, LA = π(5)(10) = 50π cm², which is approximately 157.08 cm².

Front

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

Back

LA = πrl = π(3)(4) = 12π m², which is approximately 37.70 m².

Front

What is the lateral area of a cone with a radius of 7 in and a slant height of 8 in?

Back

LA = πrl = π(7)(8) = 56π in², which is approximately 175.84 in².

Front

Calculate the surface area of a cone with a radius of 6 cm and a slant height of 10 cm.

Back

SA = πr(r + l) = π(6)(6 + 10) = π(6)(16) = 96π cm², which is approximately 301.59 cm².

Front

What is the surface area of a cone with a radius of 2 m and a slant height of 5 m?

Back

SA = πr(r + l) = π(2)(2 + 5) = π(2)(7) = 14π m², which is approximately 43.98 m².

Front

If the lateral area of a cone is 84.78 cm² and the radius is 4 cm, what is the slant height?

Back

Using LA = πrl, 84.78 = π(4)l, l = 84.78/(4π) ≈ 6.73 cm.