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What is the surface area of a cylinder whose end area is 11 and height is 11 rounded to the nearest whole number?
Imagine taking the ends off the cylinder, cutting the side down from end to end and unrolling the side; this creates a rectangle with the height of the cylinder along one edge and the circumference of the end along the other.
Thus area of side = circumference × height.
The ends of the cylinder are circles, thus:
area = π × radius²
→ radius = √(area ÷ π)
circumference = 2 × π × radius
→ circumference = 2 × π × √(area ÷ π) = 2 × √(area × π)
→ area side = 2 × √(area × π) × height
→ surface area of cylinder = 2 × area ends + area side
→ surface area = 2 × 11 units² + 2 × √(11 units² × π) × 11 units
→ surface area = 22 + 22 × √(11π) units²
→ surface area ≈ 22 + 129.33 units² ≈ 151 units²
What else can I help you with?
What is the surface area of a cylinder if the radius is 3 and the height is 11?
The surface area of a cylinder if the radius is 3 and the height is 11 equals 263.9 square units.
How do you derive of surface area of cylinder?
The surface area of a cylinder can be derived from the area of rectangle. If you 'unroll' a cylinder you have a shape of a rectangle, similar to a sheet of paper. The width of the rectangle will be the height of the cylinder and the length of the rectangle will be the circumference of the cylinder end.So, Area = length * widthwhere, width = height of cylinder & length = circumference of cylinder end = PI*(Diameter of cylinder)Therefore,surface area of a cylinder = (PI)*(diameter of cylinder)*(height of cylinder)Hope that helps!
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