Geometry SOL G.13 G.14 Area, Surface Area, Volume Study Guide Name Date Block Area, Surface Area, Volume Review and Study Guide You may use the SOL formula sheet but you must bring your own copy. Know how to: Find the area of polygons. Find missing measurements in polygons given the area of the polygon. Find compound area of figures (figures made up of more than one polygon). Find the surface area and volume of solids: prisms, cylinders, pyramids, cones, and spheres Use the SOL formula sheet to help. The formula sheet may be used on this quiz, but you must bring your own copy. Use area and volume ratios to solve problems: the ratio of perimeters is a:b, the ratio of areas is a 2 :b 2, and the area of volumes is a 3 :b 3 DO NOT LIMIT YOUR STUDYING TO PROBLEMS IN THIS STUDY GUIDE! Study questions round to the nearest hundredth if necessary: 1) Find the area of the figures below. a) b) c) d) e) f) 2) Find the value of x given the area of the figure. a) A = 70 cm 2 b) A = 80 m 2 c) A = 39 cm 2
Geometry SOL G.13 G.14 Area, Surface Area, Volume Study Guide Page 2 3) The base of a triangle is four times its height. The area of the triangle is 50 square inches. Find the base and height. 4) A parallelogram has an area of 133 ft 2 and a height of 19 feet. What is the length of the base? 5) Find the area of the shaded figure. a) b) c) 6) A robotic vacuum cleaner can clean 2 square meters of carpet in 8 minutes. About how long does it take for it to clean a carpet covering a room with the dimensions shown at right). 7) One diagonal of a kite is three times as long as the other diagonal. The area of the kite is 73.5 square yeards. What are the lengths of the diagonals? 8) Given ABCDEF ~ MNOPQR, find AB. 9) Regular hexagon I has a side length of 5 feet and an area 65 ft 2. Regular hexagon II has a perimeter of 18 feet. Find the area of hexagon II. 10) The ratio of the areas of two regular octagons is 18:25. What is the ratio of their corresponding side lengths in simplest radical form?
Geometry SOL G.13 G.14 Area, Surface Area, Volume Study Guide Page 3 11) Find the lateral area, total surface area, and volume of the figures. a) b) c) d) 12) Find the surface area and volume of the solid. 13) A cone with radius 6cm and height 12cm is filled to capacity with liquid. Find the height of a cylinder with radius 4 cm that will hold the same amount of liquid. 14) If the diameter of a soap bubble is known to be 2 mm, what is the surface area of the bubble? What is the volume? 15) A pipe is 300 cm long and has inside radius 4 cm and outside radius 5 cm. Find the volume of metal. Hint: draw a diagram. 16) The volume of a sphere is 36π. Find the surface area. 17) A pharmacist is filling medicine capsules. The capsules are cylinders with half spheres on each end. If the length of the cylinder is 12 mm and the radius is 2 mm, how many cubic mm of medication can one capsule hold? 18) The number of square centimeters in the surface area of a sphere is twice the number of cubic centimeter in the volume of a sphere. Find the radius of the sphere.
Geometry SOL G.13 G.14 Area, Surface Area, Volume Study Guide Page 4 19) A cylinder has a surface area of 1005 in 2. Find the height of the cylinder if the radius is 8 in (round to the nearest whole number). 20) A regular square pyramid is inscribed in a cone with radius 4 cm and height 4 cm. a) What is the volume of the pyramid? b) Find the slant height of the cone and the pyramid. 21) Are the figures below similar? Explain. 22) Cube C has a surface area of 36 units 2 and Cube D has a surface area of 144 units 2. Find the scale factor of C to D. 23) Two rectangular prisms are similar. Their scale factor is 3:5. For the smaller prism, the surface area is 90 cm 2 and the volume is 54 cm 3. Find the surface area and volume of the larger figure. 24) Cone A is similar to cone B. The scale factor of A:B is 2:3. The surface area and volume of cone A are 90π m 2 and 100π m 3. Find the surface area and volume of cone B (express answers in terms of π). 25) The volume of sphere A is 343π in 3 and the volume of sphere B is 8π in 3. Find the scale factor of A:B. 26) At the MetroPlex movie theater, popcorn is served in a box. At the CinemaPlex movie theater, popcorn is served in a cylindrical container. At home, Mom serves popcorn in a bowl (hemisphere in shape). Based upon the given dimensions, where are you getting the most popcorn? (Disregard the thickness of the container)
Geometry SOL G.13 G.14 Area, Surface Area, Volume Study Guide Page 5 Answer Key: 1) a) A = 924 units 2 b) A = 119 units 2 c) A = 20 units 2 d) A = 56 units 2 e) A = 98.77 units 2 f) A = 669.42 units 2 3) base = 20 inches; height = 5 inches 4) 7 ft 2) a) 14 cm b) 4 m c) 4 cm 5) a) 672 units 2 b) 75 m 2 c ) 65 units 2 6) 244 minutes (about 4 hours) (area of figure is 61 m 2 ) 7) 7 yd, 21 yd 8) 10.67 cm 9) 23.4 ft 2 10) 3 2 : 5 11) a) LA = 24 in 2 ; SA = 36 in 2 ; V = 12 in 3 12) SA = 1992.31 ft 2 ; V = 5625 ft 3 b) LA = 219.91 cm 2 ; SA = 376.99 cm 2 ; V = 549.78 cm 3 c) LA = 490.09 cm 2 ; SA = 94.48 cm 2 ; V = 2261.95 cm 3 d) LA = 188.68 units 2 ; SA = 288.68 units 2 ; V = 266.67 units 3 13) 9 cm 14) SA = 12.57 mm 2 ; V = 4.19 mm 3 15) 8482.30 cm 3 16) 108π 339.29 units 2 17) 184.31 mm 3 18) 1.5 cm 19) 12 in 20) a) 42.67 cm 3 b) lcone 5.66 cm; lpyramid 4.90 cm 21) No, because the radii and heights have 22) sf is 1:2 1 1 different scale factors ( and 3 2 respectively). 23) SA = 250 cm 2 ; V = 250 cm 3 24) SA = 202.5π m 2 ; V = 337.5 π m 3 25) 7:2 26) V box =200 in 3 ; V cylinder =226.19 in 3 ; V bowl = 261.8 in 3 ; - get most popcorn from the bowl