SOLUTION: How do you Find the surface area to the nearest whole unit of a cylinder and a Cone? Can I get both explained separately step by step?
Thank you
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Question 459131: How do you Find the surface area to the nearest whole unit of a cylinder and a Cone? Can I get both explained separately step by step?
Thank you
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
A cylinder (assume radius r and height h) is composed of two circular bases and some "remaining" surface area. The area of each circular base is obviously 
, so this component of the surface area is 
.
The remaining part of the surface area (sometimes called "lateral area") is a rectangle when unfolded. The height of this rectangle is h. The base of the rectangle is the exact same as the circumference of the base (visualize the unfolding of the cylinder and you will see why). Hence, this area is (h))
.
Add these two areas to get )
.
-----------------
For a cone with radius r, height h, the surface area is composed of a circle (area = ) and the lateral area. Finding the lateral area is a bit difficult to visualize, but if you were to unfold the cone, you would get part of a circle of radius 
. This fraction is equal to the ratio of the circumference of the part-circle to the circumference of the whole circle, namely 
. The lateral area is hence ^2 \frac{r}{\sqrt{r^2+h^2}} = \pi r \sqrt{r^2+h^2})
Add these two and you have the surface area of a cone.
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