Lateral Area & Surface Area Of Cylinders Geometry 10:2

Notes Using the Word Bank, label the parts of the net for a right cylinder.

Notes: LATERAL AREA In a cylinder, the lateral area is the lateral or side surface of the solid but it is the shape of a rectangle in the net.

Notes: Total Surface Area The total surface area of a cylinder will include the lateral surface (the rectangle in the net) and the two bases which are in the shape of a circle.

Example: Lateral Area: 2πrh 2×π×3 = 6π ≈ 18.8495 6π × 7 =42π ≈ 131.9 Total Surface Area: 2πrh + 2(πr²) 42π + 2(π3²) = 60π ≈ 180.5

Example: Lateral Area: 2πrh The radius is 7 since both legs are the radius of the circle. 14π ≈ 43.98 14π × 5 = 70π ≈ 219.9 ft² Total Surface Area: 2πrh + 2(πr²) 70π + 7²π = 70π + 49π = 119π ≈373.8 ft²

Example: Lateral Area: 2πrh Since the hypotenuse is 10 then the radius is 52 102 π × 4 ≈ 44.4 × 4 ≈ 177.7 Total Surface Area: 2πrh + 2(πr²) 402 π + 2∙π(52)² 402 π + 2(50π) ≈ 491.9cm²

Example: Lateral Area: P∙h 8 × 6 × 11 = 528 in² Total Surface Area: P∙h + B (360÷6÷2) = 30 4 ÷ tan(30) = 6.9 Area of this hexagon is 166.2768 × 2 = 332.6 528 + 332.6 = 860.6