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The circumference of the base of a right circular cylinder is 176 cm. If the height of the cylinder is 1 m, find the lateral surface area of the cylinder.

Answer :

To find the lateral surface area of a right circular cylinder with a circumference of 176 cm and height of 1 m, calculate the radius from the circumference, convert the height into cm, and use the formula A=2πRL, resulting in an area of 17600 cm extsuperscript{2}.

The goal is to find the lateral surface area of a right circular cylinder with a given circumference and height. To do this, we use the relationship that the lateral surface area can be conceptualized as the area of a rectangle that is formed when 'unwrapping' the cylinder's side. The height of this rectangle is the height of the cylinder, L, and the width is the circumference of the base of the cylinder.

The circumference is provided as 176 cm, which allows us to find the radius R as follows:

  1. Circumference (C) = 2πR => R = C/(2π).
  2. Radius (R) = 176 cm / (2π) cm.

However, since the height of the cylinder is given in meters, we need to convert the height L into centimeters:

  1. Height (L) = 1 m = 100 cm.

Now, we can calculate the lateral surface area using the formula A = 2πRL:

  1. Lateral Surface Area (A) = 2π imes R imes L.
  2. A = 2π imes (176/(2π)) imes 100.
  3. A = 176 imes 100 = 17600 cm2.

Hence, the lateral surface area of the cylinder is 17600 cm2.

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