The lateral surface area of a cylinder is calculated using the formula 2πrh, where r is the radius and h is the height. The total surface area is calculated using the formula 2πr² + 2πrh.
Find the lateral and total surface areas of each cylinder.
To find the surface area of a cylinder, we need to find the areas of the top and bottom bases, as well as the lateral surface area. The lateral surface area is the area of the curved side of the cylinder.
Cylinder 1:
Lateral surface area: 2πrh = 2π(3 cm)(5 cm) = 30π cm²
Total surface area: 2πr² + 2πrh = 2π(3 cm²) + 2π(3 cm)(5 cm) = 66π cm²
Cylinder 2:
Lateral surface area: 2πrh = 2π(4 ft)(10 ft) = 80π ft²
Total surface area: 2πr² + 2πrh = 2π(4 ft²) + 2π(4 ft)(10 ft) = 128π ft²
Cylinder 3:
Lateral surface area: 2πrh = 2π(7 cm)(20 cm) = 280π cm²
Total surface area: 2πr² + 2πrh = 2π(7 cm²) + 2π(7 cm)(20 cm) = 508π cm²
Cylinder 4:
Lateral surface area: 2πrh = 2π(6.5 m)(9 m) = 117π m²
Total surface area: 2πr² + 2πrh = 2π(6.5 m²) + 2π(6.5 m)(9 m) = 234π m²