Final answer:
In solving for the radius of a cylinder given the surface area and height, we substitute these values into the formula for the surface area of a closed cylinder, rearrange the equation to solve for radius and find the approximate value of 'r' as 5 cm.
Step-by-step explanation:
The subject of this question is Mathematics, and it's appropriate for a High School level. The calculation will be done using the formula for the surface area of a closed cylinder, which is 2πr(h + r), where r is the radius and h is the height.
Given the surface area as 376.99 cm² and height as 7 cm, the equation can be rearranged to solve for the radius:
- Firstly, substitute the provided values into the formula: 376.99 = 2πr(7 + r)
- Next, divide both sides of the equation by 2π and 7. Simplifying gives us 376.99/2π7 = r + r²
- By simplifying further, you will find that r (or radius) equals approximately 5 cm. Hence the correct answer is choice b.
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