Geometry question I still don’t understand. Please walk me through this.

Question

Determine the exact total surface area of the hemisphere attached to the cylinder:

from top to bottom, the cylinder is 30 cm, and the radius of the hemisphere is 4 cm.

Answer 1

Hi Deinonychus A.

I have posted a video on my YouTube channel called Mr. A's Physics. Since you are asking for further explanation, I figured it might be better to explain verbally and with demonstration.

Please go to YouTube, visit my channel and take a look at the solution.

If you need further clarification on this or any other problem, feel free to send me a message via Wyzant.

I also offer one-on-one tutoring in case you or someone you know needs help.

Mr. A (Frank Ansari)

Answer 2

You want to break the problem into parts. There are three areas we need to find:

1. Lateral surface area of the cylinder (2*pi*r*h, h is height (30 cm), r is radius (4cm)).
2. Area of base of cylinder, which is a disk (pi*r^2)
3. Area of hemisphere (2*pi*r^2).

Then, just add together these three areas.