Name Period No. Geometry Unit Review with Application Problems
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1 Name Period No. Geometry Unit Review with Application Problems For problems 1-3, find the area of each figure. Show all steps. 1) 2) 4) Draw a parallelogram with an area of 50 sq. units in the 3) coordinate plane. Show steps to prove accuracy.
2 For problems 5 and 6, find the unknown value labeled x on each figure. Show formula, substitution, and answer steps. 5) The rectangle shown has an area of 80 sq. units. 6) The trapezoid shown has an area of 115 sq. units. 7) Jeff s landscaping business makes odd-shaped gardens that include semicircles. The radius of the flower bed below is 2.5 m. a. Find the length of the edging material needed to border the ENTIRE flower bed. Use 3.14 for π. Show all work. b. What is the area of the flower bed? Show all steps. Leave your final answer in terms of π. 8) A machine shop has a square metal plate with sides that measure 4 cm each. An employee must cut four semicircles with a radius of! cm and four quarter circles with a radius of 1 cm from its sides and corners. " What is the area of the plate formed? Show all steps. Use "" for π. %
3 9) If one circle has a diameter of 10 cm and a second circle has a diameter of 20 cm, what is the ratio of the area of the larger circle to the area of the smaller circle? Show all work. For problems 10-13, find the area of the shaded region. Show all work. 10) 11) 12) 13)
4 14) Find the area of the UNSHADED region. Show all work. For problems 15 and 16, name the figure represented by the net. Next, highlight the perimeter of the entire lateral area. Finally, find the surface area of the figure using the S = LA + 2B formula. 15) 16)
5 17) Given a cube with edges that are & inch long: ' a. Find the surface area of the cube. Show your work. b. Lydia makes a scale drawing of the cube using a scale factor of 4. Find the surface area of the cube that Lydia drew. Show your work. c. What is the ratio of the surface area of the scale drawing to the surface area of the actual cube? How does the value of the ratio compare to the scale factor? For problems 18 and 19, find the surface area of the prisms using the SA = LA + 2B formula. Then find the volume using the V = Bh formula. 18) 19)
6 For problems 20 and 21, find the volume of the solids. Show all work. 20) 21) 22) In the diagram, there are 14 cubes glued together to form a solid. Each cube has a volume of! ( in&. Find the surface area of the solid. 23) The surface area of a rectangular prism is 68 " & in ". The dimensions of its base are 3 in. by 7 in. Use the formula SA = LA + 2B and LA = ph to find the unknown height h of the prism.
7 24) Substitute the given values into the formula for each diagram. Then solve for the missing side. Show all steps. Area = 22 in 2 a) b)? Volume = in3 25) A concrete block has a cylindrical hole 4 feet in diameter drilled through it to allow a pipe to pass through. How many cubic feet of concrete are left in the block? Round your answer to the nearest tenth. Show all work.
8 26) Find the surface area and volume of the figure below. Show all work. 27) What is the volume left in the cylinder after the shaded cone region is removed? Show all work. 28) Find the volume of the solid after the square pyramid has been removed. Show all work. 29) Air is leaking from an advertising balloon in the shape of a sphere at a rate of 26 cubic feet per minute. If the radius of the balloon is 7 feet, how long would it take for the balloon to empty completely? Use 3.14 for π. Round your answer to the nearest minute.
9 30) 31) You want to fill the top part of an hourglass " full of salt. The height of the hourglass is 20 cm, and the & radius of the base is 8 cm. Find the volume of salt needed. 32) A cylindrical tank (with dimensions shown below) contains water that is 1-foot deep. If water is poured into the tank at a constant rate of 20?@A, will the tank overflow? Use 3.14 for π. BCD
10 33) The dimensions of several right rectangular fish tanks are listed below. Find the volume in cubic centimeters, the capacity in liters (1 L = 1,000 cm & ), and the surface area in square centimeters for each tank. What do you observe about the change in volume compared with the change in surface area between the small tank and the extra-large tank? 34) A rectangular container 15 com long by 25 cm wide contains 2.5 L of water. a. Find the height of the water level in the container. (1L = 1000 cm & ) 15 cm 25 cm b. If the height of the container is 18 cm, how many more liters of water would it take to completely fill the container? Show your work. c. What percentage of the tank is filled when it contains 2.5 L of water?
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