If the surface area of a cylinder is 150π cm² and the height is 10 cm, what is the radius?

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Q: If the surface area of a cylinder is 150π cm² and the height is 10 cm, what is the radius?

Solution: The surface area of a cylinder is given by SA = 2πr(h + r). Setting 150π = 2πr(10 + r), we find r = 5 cm.

Steps: 10

Step 1: Write down the formula for the surface area of a cylinder: SA = 2πr(h + r).
Step 2: Substitute the given surface area (150π) and height (10 cm) into the formula: 150π = 2πr(10 + r).
Step 3: Divide both sides of the equation by π to simplify: 150 = 2r(10 + r).
Step 4: Expand the right side of the equation: 150 = 20r + 2r².
Step 5: Rearrange the equation to set it to zero: 2r² + 20r - 150 = 0.
Step 6: Divide the entire equation by 2 to make it simpler: r² + 10r - 75 = 0.
Step 7: Factor the quadratic equation: (r + 15)(r - 5) = 0.
Step 8: Set each factor to zero: r + 15 = 0 or r - 5 = 0.
Step 9: Solve for r: r = -15 (not valid since radius can't be negative) or r = 5.
Step 10: Conclude that the radius of the cylinder is 5 cm.