Final answer:
The area of one of the circular faces of a cylinder with a radius of 15 cm is 707 cm², the curved surface area is 2715 cm², and the height is 29 cm, with each answer rounded to the nearest integer.
Step-by-step explanation:
To solve for the area of one of the circular faces of the cylinder with a given total surface area of 4129 cm² and a radius of 15 cm, we start by using the formula for the area of a circle: A = πr². Plugging in the radius, we calculate:
A = π(15 cm)²
= π(225 cm²)
= 706.858 cm² (to three decimal places)
To find the curved surface area of the cylinder, we take the total surface area and subtract the areas of the two circular faces. Thus:
Curved surface area = Total surface area - 2 × Area of one circular face
= 4129 cm² - 2(706.858 cm²)
= 4129 cm² - 1413.716 cm²
= 2715.284 cm²
Finally, to find the height of the cylinder, we use the formula for the curved surface area which is also the lateral surface area: Curved surface area = 2πrh. Solving for h:
h = Curved surface area / (2πr)
= 2715.284 cm² / (2π(15 cm))
= 2715.284 cm² / (94.247 cm)
= 28.822 cm
All answers are to the nearest integer: The area of one circular face is 707 cm², the curved surface area is 2715 cm², and the height of the cylinder is 29 cm.