How Do You Calculate the Surface Area of an Enlarged Cylinder?

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SUMMARY

The discussion focuses on calculating the surface area of an enlarged cylinder with a volume of 400 cm³ and a height of 10 cm, scaled by a factor of 2. The surface area formula for a cylinder is established as 2πr² + 2πrh, where r is the radius. To find the radius, users can derive it from the volume formula, V = πr²h. After determining the original cylinder's surface area, it is multiplied by 4 (the square of the scale factor) to find the surface area of the enlarged cylinder.

PREREQUISITES
  • Understanding of cylinder volume formula (V = πr²h)
  • Knowledge of surface area formula for a cylinder (SA = 2πr² + 2πrh)
  • Ability to manipulate algebraic equations to solve for radius
  • Familiarity with scale factors in geometric transformations
NEXT STEPS
  • Learn how to derive the radius from the volume of a cylinder
  • Study the impact of scale factors on surface area and volume
  • Explore geometric transformations and their applications
  • Practice calculating surface areas of various geometric shapes
USEFUL FOR

Students studying geometry, educators teaching mathematical concepts, and anyone interested in understanding the properties of cylinders and geometric scaling.

Elizabeth12
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The volume of the cylinder is 400 cm cubed. Calculate the surface area of a similar cylinder formed by enlarging the one shown by a scale factor of 2. The height of the cylinder is 10 cm.

I don't know how to calculate the surface area, but I know that the area factor is (H/h)squared.

Please help me out!
 
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Elizabeth12 said:
The volume of the cylinder is 400 cm cubed. Calculate the surface area of a similar cylinder formed by enlarging the one shown by a scale factor of 2. The height of the cylinder is 10 cm.
If there was a diagram attached, I do not see it. Can you attach one?

Elizabeth12 said:
I don't know how to calculate the surface area, but I know that the area factor is (H/h)squared.
You can find the formula if you do a Google search.
 
Hi Elizabeth! :smile:
Elizabeth12 said:
I don't know how to calculate the surface area …

The surface is two circles and a rectangle. :wink:
 
The volume of a cylinder is [math]\pi r^2h[/math]. If your original cylinder has height 10 and volume 400, you can calculate it radius from that.

The surface area is [math]2\pi r^2+ 2\pi rh[/math]. The first [math]2\pi r^2[/math] is the area of the two circles tiny-tim mentioned- the two ends of the cylinder. If you imagine cutting the cylinder down its length, you can unfold it into the rectangle tiny-tim mentioned. One side is the height of the cylinder, h, the other is the circumference of the circular end, [math]2\pi r[/math]. Its area is the remaining [math]2\pi rh[/math].

Once you have both height and radius of the given cylinder, you can calculate its surface area, then multiply that by [math]2^2= 4[/math].
 
Thank you for your help!
 

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