Final answer:
The radius of a cylinder with a height of 21 cm and a curved surface area of 264 m² is approximately 2 meters after converting the height into meters and using the formula for the curved surface area (A = 2πrh).
Step-by-step explanation:
The question provided is focusing on finding the radius of a cylinder with given measurements for height and curved surface area. The key formula to use here is the area formula for the curved surface area of a cylinder, which is A = 2πrh, where 'A' is the curved surface area, 'r' is the radius, and 'h' is the height.
In this case, we're given that the height (h) is 21 cm, which we must convert into meters since the curved surface area is given in square meters (noted as 264 m²). So, h becomes 0.21 m. Now, we use the curved surface area given and plug it into the formula to solve for 'r'.
- Convert the height from cm to m: 21 cm = 0.21 m
- Write the formula for curved surface area: A = 2πrh
- Plug in the known values: 264 m² = 2πr(0.21 m)
- Rearrange the formula to solve for r: r = â– 264 m² / (2π â– 0.21 m)
- Calculate the radius: r ≤ 2 m (after rounding to the nearest whole number, as the answer choices are in whole meters)
After completing the calculation, you will find that the radius of the cylinder is approximately 2 meters, hence the answer is Option A, 2 m.