Final answer:
To find the minimum square cm of paper needed to cover the curved surface area of the cylinder, we first need to calculate the curved surface area. Given that the height of the cylinder is twice the radius and the volume is 17248 cm³, we can calculate the value of the radius. Substituting the value of 'r' in the formula for the curved surface area, we find that the minimum square cm of paper needed is approximately 5027 cm².
Step-by-step explanation:
To find the minimum square cm of paper needed to cover the curved surface area of the cylinder, we first need to calculate the curved surface area.
The formula for the curved surface area of a cylinder is:
A = 2πrh
Given that the height of the cylinder is twice the radius and the volume is 17248 cm³, we can calculate the value of the radius.
Let's assume the radius of the cylinder is 'r'.
Since the height is twice the radius, the height can be represented as '2r'.
Given that the volume of the cylinder is 17248 cm³, we can write the equation:
17248 = πr²(2r)
Simplifying the equation, we get:
2πr³ = 17248
Dividing both sides by 2π, we get:
r³ = 8648
Taking the cube root of both sides, we get:
r = 20
Now, substituting the value of 'r' in the formula for the curved surface area, we get:
A = 2πrh = 2π × 20 × 40 = 1600π cm²
Therefore, the minimum square cm of paper needed to cover the curved surface area of the cylinder is approximately 5027 cm².