Question Video: Calculating the Base Diameter of a Cylinder given Its Lateral Surface Area and Its Height | Nagwa Question Video: Calculating the Base Diameter of a Cylinder given Its Lateral Surface Area and Its Height | Nagwa

# Question Video: Calculating the Base Diameter of a Cylinder given Its Lateral Surface Area and Its Height Mathematics • Second Year of Preparatory School

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Find the diameter of the base of a cylinder if the lateral surface area is 434π square centimeters and the height is 31 centimeters.

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### Video Transcript

Find the diameter of the base of a cylinder if the lateral surface area is 434π square centimeters and the height is 31 centimeters.

Weβve been given the lateral surface area of a cylinder, along with its height, and asked to determine the diameter of the cylinderβs circular base. Letβs begin by recalling how the lateral surface area is calculated.

The lateral surface area of a cylinder is the area of the curved surface that wraps around the cylinder. This surface is a rectangle, with a length equal to the circumference of the circular base and a width equal to the height of the cylinder. The area of this surface is therefore equal to two ππβ. We can substitute the lateral surface area of 434π and the height of 31 to give the equation 434π equals two ππ multiplied by 31.

Now, as it is the diameter of the circular base that weβre asked to calculate, and we know that the diameter is always twice the radius, we can replace two π with π to give an equation in terms of π. Alternatively, we could solve our previous equation for π and double its value at the end.

To solve our equation for π, we can first cancel a factor of π from both sides to give 434 is equal to 31π. Finally, we divide both sides of the equation by 31. And we have that π is equal to 14. Including the length units, weβve found that the diameter of the base of the given cylinder is 14 centimeters.

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