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

[Elizabeth12]

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!

 

[eumyang]

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?

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.

 

[tiny-tim]

Hi Elizabeth!

I don't know how to calculate the surface area …

The surface is two circles and a rectangle.

 

[HallsofIvy]

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].

 

[Elizabeth12]

Thank you for your help!