5. The lateral surface area of a hollow cylinder is 4224 cm2. It is cut along its height and formed a rectangular sheet of width 33 cm. find the perimeter of rectangular sheet.

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Let's denote the hollow cylinder's outer radius as RR, inner radius as rr, and height as hh. The lateral surface area (LSA) of a hollow cylinder is given by the formula: LSA=2πh(R+r)LSA=2πh(R+r) In this case, the LSA is given as 4224 cm²: 4224=2πh(R+r)4224=2πh(R+r) Now, the rectangular...
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Let's denote the hollow cylinder's outer radius as RR, inner radius as rr, and height as hh. The lateral surface area (LSA) of a hollow cylinder is given by the formula: LSA=2πh(R+r)LSA=2πh(R+r) In this case, the LSA is given as 4224 cm²: 4224=2πh(R+r)4224=2πh(R+r) Now, the rectangular sheet is formed by cutting along the height of the hollow cylinder. The width of the rectangular sheet is given as 33 cm. The width of the rectangular sheet is equal to the height of the hollow cylinder (hh). Therefore, h=33h=33 cm. Now, we can rearrange the formula for LSA to find R+rR+r: R+r=LSA2πhR+r=2πhLSA Substitute the given values: R+r=42242π×33R+r=2π×334224 Now, to find the perimeter of the rectangular sheet, we use the formula: Perimeter=2(Length+Width)Perimeter=2(Length+Width) Since the width is given as 33 cm, and the length is equal to the outer circumference of the hollow cylinder, we find the outer circumference using C=2πRC=2πR: Length=2πRLength=2πR Substitute the values and calculate: Length=2π×(42242π×33)Length=2π×(2π×334224) Now, plug the values into the perimeter formula: Perimeter=2(2π×(42242π×33)+33)Perimeter=2(2π×(2π×334224)+33) Simplify to get the numerical value. Keep in mind that ππ is approximately 3.14 for calculation purposes. read less
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