The surface area of the vase is in. \( ^{2} \). (Type an exact answer in terms of \( \mathrm{Pi} \pi \).)

Imagine a beautifully crafted vase, its elegant curves and contours providing ample surface area to work with! To find the surface area, we start with the formula for a cylinder, which is \( 2\pi r(h + r) \), where \( r \) is the radius and \( h \) is the height. If you have the dimensions, just plug them into the formula, and voila! You get the surface area in terms of \( \pi \), which not only looks neat but also preserves the exactness of your answer! But wait, don’t forget about the common mistakes! Many folks get tangled up with taking the radius and height from different parts of the vase or forgetting to add both the top and bottom. Remember, consistency is key! Always double-check that you’re measuring from the same reference point. Happy calculating!