Answer :
The lateral surface area of the cylinder is approximately 17,600 cm², calculated using the formula A = 2πrL with the radius found from the given circumference of the base, and the height converted to centimeters.
The question asks for the lateral surface area of a right circular cylinder with a known circumference of its base and a height of 1 meter. To find the lateral surface area, we can use the formula A = 2πrL, where r is the radius of the base and L is the height of the cylinder.
Since the circumference C is given by C = 2πr, we can solve for r and then use this value to find A. First, divide the circumference by 2π: r = C / (2π) = 176cm / (2π).
Next, convert the height from meters to centimeters to match the units of the circumference: L = 1m = 100cm.
Finally, substitute these values into the lateral surface area formula to find the answer.
In this case:
r = 176cm / (2π) approximately 28cm,
L = 100cm,
A = 2π(28cm)(100cm) = 5600π cm2, which is approximately 17,600 cm2 to the nearest whole number.
