Surface Area of Cylinders and Cones

Front

What is the surface area formula for a cone?

Back

SA = \pi rl + \pi r^2

Front

What is the surface area formula for a cylinder?

Back

SA = 2\pi rh + 2\pi r^2

Front

How do you calculate the height of a cylinder given its surface area and radius?

Back

Rearrange the surface area formula: h = (SA - 2\pi r^2) / (2\pi r)

Front

What is the slant height of a cone?

Back

The slant height (l) is the distance from the base of the cone to the apex along the side.

Front

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

Back

Lateral SA = \pi rl

Front

How do you find the total surface area of a cylinder?

Back

Total SA = Lateral SA + Area of the two bases = 2\pi rh + 2\pi r^2

Front

What is the formula for the volume of a cylinder?

Back

Volume = \pi r^2 h

Front

What is the formula for the volume of a cone?

Back

Volume = \frac{1}{3}\pi r^2 h

Front

If a cylinder has a radius of 3 cm and a height of 5 cm, what is its surface area?

Back

SA = 2\pi(3)(5) + 2\pi(3^2) = 54\pi \approx 169.65 cm^2

Front

What is the relationship between the radius and height of a cylinder in terms of surface area?

Back

As the radius increases, the height must decrease to maintain a constant surface area, and vice versa.