Surface area of cylinders, cones, and spheres

Front

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

Back

The surface area (SA) of a cylinder is given by the formula: SA = 2πr(h + r), where r is the radius and h is the 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(l + r), where r is the radius and l is the slant height.

Front

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

Back

The surface area (SA) of a sphere is given by the formula: SA = 4πr², where r is the radius.

Front

How do you calculate the radius from the diameter?

Back

The radius (r) is half of the diameter (d): r = d/2.

Front

If a cylinder has a height of 10 inches and a radius of 3 inches, what is its surface area?

Back

SA = 2π(3)(10 + 3) = 2π(3)(13) = 78π ≈ 245.04 in².

Front

What is the surface area of a sphere with a radius of 5 inches?

Back

SA = 4π(5)² = 4π(25) = 100π ≈ 314.16 in².

Front

What is the slant height of a cone if the height is 4 inches and the radius is 3 inches?

Back

Use the Pythagorean theorem: l = √(r² + h²) = √(3² + 4²) = √(9 + 16) = √25 = 5 inches.

Front

How much material is needed for a cylinder with a height of 6 inches and a diameter of 4 inches?

Back

SA = 2π(2)(6) + 2π(2)² = 24π + 8π = 32π ≈ 100.48 in².

Front

What is the total surface area of a cone with a radius of 3 inches and a slant height of 5 inches?

Back

SA = π(3)(5) + π(3)² = 15π + 9π = 24π ≈ 75.36 in².

Front

If a sphere has a surface area of 314 in², what is its radius?

Back

Using the formula SA = 4πr², we have 314 = 4πr². Solving for r gives r ≈ 5 inches.