Question
Download Solution PDFThe curved surface area of a right circular cylinder and a sphere are equal. If the radius of the sphere and cylinder are 2 and 3, respectively, then find the total surface area of the cylinder.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Radius of the sphere, r = 2
Radius of the cylinder, R = 3
The curved surface area of a right circular cylinder = The curved surface area of a sphere
Formula used:
The curved surface area of a cylinder = 2πRh
The curved surface area of a sphere = 4πr2
Where r = radius of the sphere , R = radius of the cylinder
And, h = the height of a cylinder
Calculation:
According to question
⇒ 2πRh = 4πr2
⇒ 2π × (3) × h = 4π × (2)2
⇒ h = 8/3
The total surface area of the cylinder = 2πR(R + h)
⇒ 2π(3)(3 + 8/3) = 34π unit
∴ Correct answer is 34π unit.
Last updated on Jun 19, 2025
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