Geometry / Mr. Hansen 4/14/2004

Name: _________KEY_________

Volume and Surface Area Quiz

Instructions: Show your work clearly. Leave answers in simple pi or radical form, with units. No calculator is permitted.
A rectangular solid (box) is glued to the top of a right cylindrical kiosk as shown. The box has dimensions 20 cm by 30 cm by 5 cm. Find both the volume and the total surface area of the resulting solid.
	The first answer (volume) is straightforward: Vsolid = Vcyl + Vbox           = βhcyl + lwhbox           = pr^2hcyl + 20(30)(5)           = p(400)^2(1000) + 3000           = p(16)(10 million)) + 3000           = (160,000,000p + 3000) cubic cm
For the area, the key insight is to think of the box as being “pushed up” from the interior of the kiosk. How much additional wrapping paper is needed to wrap the entire object? Since the top of the box is already covered even before the box is pushed up, the additional paper is needed only on the 4 lateral faces of the box, not on the top or bottom of the box.
TSAsolid = TSAcyl + LSAbox                = phcyl + 2pr^2 + left face + right face + front face + back face                 = 2prhcyl + 2pr^2 + 2(20)(5) + 2(30)(5)                 = 2p(400)(1000) + 2p(400)^2 + 2(100) + 2(150)                 = 2p(400,000 + 160,000) + 200 + 300                 = 2p(560,000) + 500                 = (1,120,000p + 500) square cm