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 \(\displaystyle \pi r^2h\). If your original cylinder has height 10 and volume 400, you can calculate it radius from that.

The surface area is \(\displaystyle 2\pi r^2+ 2\pi rh\). The first \(\displaystyle 2\pi r^2\) 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, \(\displaystyle 2\pi r\). Its area is the remaining \(\displaystyle 2\pi rh\).

Once you have both height and radius of the given cylinder, you can calculate its surface area, then multiply that by \(\displaystyle 2^2= 4\).

 

[Elizabeth12]

Thank you for your help!