12.2 Surface Areas of Prisms and Cylinders
Name _________________________________
Learning Objective: After this lesson, you should be able to successfully find the lateral area and surface area
of prisms and cylinders.
Standard: G.MG.1 Use geometric shapes, their measures, and their properties to describe objects.
G.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and
identify three-dimensional objects generated by rotations of two-dimensional objects.
G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a
circle, volume of a cylinder, pyramid, and cone.
G.MG.2 Apply concepts of density based on area and volume in modeling situations
Exercises - Find the lateral area and surface area of each prism. HINT: Base is darkened!!
Round to the nearest tenth if necessary.
1.
Perimeter of base = __________
Height of prism (dist between bases) = ____
LA = ____________
Area of Base (trapezoid) = ______
SA = ______________
2. Total SA only. (6 rectangles)
Surface area = __________
3. Find LA only!
Perimeter o f base = __________
Height (dist between bases) = ______
LA = __________________
12.2 Practice on Surface Areas of Prisms and Cylinders
Find the lateral area and surface area of each prism. Round to the nearest tenth if necessary.
1.
Total Surface area = ________________
2.
Total Surface area = ________________
3.
4.
Perimeter of base = __________
Perimeter of base = __________
Height of prism (dist between bases) = ____
Height of prism (dist between bases) = ____
LA = ____________
LA = ____________
Area of Base (triangle) =
___________
SA = ______________
Area of Base (triangle) = _____________
SA = ______________
5.
Perimeter of base = __________
Height (dist between bases) = ______
LA = __________________
Find the lateral area and surface area of each cylinder. Round to the nearest tenth.
6.
r = ____ h = _____
LA = ______________
SA = ____________________
r = ____ h = _____
LA = ______________
SA = ____________________
7.
8.
r = ____ h = _____
LA = ______________
SA = ____________________
r = ____ h = _____
LA = ______________
SA = ____________________
9.
10. CAKES A cake is a rectangular prism with height 4 inches and base 12 inches by 15 inches. Wallace
wants to apply frosting to the sides and the top of the cake. What is the surface area of the part of the cake that
will have frosting?
11. EXHAUST PIPES An exhaust pipe is shaped like a cylinder with a height of 50 inches and a radius of 2
inches. What is the lateral surface area of the exhaust pipe? Round your answer to the nearest hundredth.
12. TOWERS A circular tower is made by placing one cylinder on top of another. Both cylinders have a height
of 18 inches. The top cylinder has a radius of 18 inches and the bottom cylinder has a radius of 36 inches.
What is the total surface area of the tower? Round your answer to the nearest hundredth.
Answers: 1. 768 yd2
3. 24 in, 5 in, 120 in2, 24 in2, 168 in2
7. 2 m, 2 m, 25.1 m2, 50.2 m2
5. 13yd, 9.5 yd, 123.5 yd2
9. 8 in, 12 in, 602.9 in2, 1004.8 in2
11. 628 in2