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A right cylinder has a circumference of 97 cm. Its height is twice the radius. Identify the lateral area and the surface area of the cylinder?

User Jaael
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Final answer:

The lateral area and surface area of a cylinder can be computed using its circumference and height. With the given circumference of 97 cm, the estimated lateral area is approximately 2992.3651 cm² and the surface area is approximately 3961.0659 cm².

Step-by-step explanation:

The question deals with finding the lateral area and the surface area of a right cylinder when the circumference and the height-to-radius ratio are given. The circumference (C) of a cylinder is given by the formula C = 2πr, where r is the radius. Given C = 97 cm, we can solve for r:

r = C / (2π) = 97 / (2π) = 15.4318 cm (approximately),

Since the height is twice the radius,

h = 2r = 2 × 15.4318 cm = 30.8636 cm (approximately).

The lateral area (LA) of the cylinder is the perimeter of the base times the height, given by the formula LA = 2πrh. Plugging in the values, we find:

LA = 2π × 15.4318 cm × 30.8636 cm = 2992.3651 cm² (approximately).

The surface area (SA) of a cylinder is calculated by adding the areas of the two bases to the lateral area, SA = 2πr² + LA. Therefore,

SA = 2π × (15.4318 cm)² + 2992.3651 cm² = 3961.0659 cm² (approximately).

User Darrel Holt
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