what is the surface area of a cylinder with the radius of 5 and height of 11
You can imagine the surface area like a piece of paper wrapped up into a scroll with two circles taped to the bottom and top. Then all you need to do is multiply the length by the height of that rectangular piece of paper, and then add the areas of the two circles. That is all the formula for a cylinder is. The length is the circumference of one of the circles at the bottom, and the height is the height of the cylinder.
First lets find the area of the rolled up rectangular piece of paper.
A1=L*H
H=11
L= the circumference of the circle at the top or bottom. Circumference is pi times the diameter. The diameter is two times the radius. The radius is 5. So the cirumference is pi times 10. L = 10π.
A1 = 110π
Second lets find the area of the top and bottom circles.
The area of a circle is πr2
Since both circles are the same size, we can multiply the area of one of them by two.
A2 = 2(π)(52)
A2 = 50π
Now add A1 and A2
110π + 50π = 160π
+26388 what is the surface area of a cylinder with the radius of 5 and height of 11
Let A = surface area
Let r = radius
Let h = height
\(\begin{array}{|rcll|} \hline A &=& (2\pi r)\cdot h + 2\cdot (\pi r^2) \\ A &=& (2\pi r)\cdot (h + r) \quad & | \quad r = 5 \qquad h = 11 \\ A &=& (2\pi 5)\cdot (11 + 5) \\ A &=& 10\cdot \pi\cdot 16 \\ A &=& 160\cdot \pi \\ A &=& 502.654824574 \\ \hline \end{array}\)
