Final answer:
The total surface area of the cylinder is approximately 334796cm² (Option E). To find the total surface area of the cylinder, calculate the radius and height of the cylinder based on the given ratio. Then, use the formula A = 2πrh + 2πr² to find the total surface area.
Step-by-step explanation:
To find the total surface area of the cylinder, we need to find the radius and height of the cylinder.
Let's assume the radius is 7x and the height is 2x.
Since the volume of the cylinder is given as 6062364 cm³, we can use the formula for the volume of a cylinder V = πr²h.
Substituting the values, we get 6062364 = π(7x)²(2x).
Solving for x, we find x = 12.
Now we can calculate the radius and height of the cylinder. T
he radius is 7(12) = 84 cm and the height is 2(12) = 24 cm.
The total surface area of the cylinder can be calculated using the formula A = 2πrh + 2πr², where r is the radius and h is the height.
Substituting the values, we get A = 2π(84)(24) + 2π(84)².
Simplifying this expression, we find that the total surface area of the cylinder is 50176π + 56448π = 106624π cm².
To find the approximate value, we can use the approximation π ≈ 3.142.
Therefore, the total surface area of the cylinder is approximately 334796 cm² (Option E).
The complete question is: The radius and height of a cylinder are in the ratio 7:2. If the volume of the cylinder is 6062364 cm³, find the total surface area of the cylinder.
A) 54238 cm²
B) 72342 cm²
C) 87426 cm²
D) 98134 cm²
E) 334796 cm²