Name _____________________________________________ Date _______ End of Module 3 Review (3.1 to 3.11) CC Geometry For numbers 1 – 10, find the Volume. If necessary, leave your answer in terms of S or in simplest radical form. 1) 2) 3) Cube

4) 5) 6)

Answer key

7)

9)

8) 10) 11) The figures below show two polygonal regions used to approximate the area of the region inside an ellipse.

Find the average estimate for the area of the ellipse.

12) A window is made up of a single piece of glass in the shape of a semicircle and a rectangle, as shown in the diagram below. Tess is decorating for a party and wants to put a string of lights all the way around the outside edge of the window. To the nearest foot, what is the length of the string of lights that Tess will need to decorate the window?

13) In the diagram below, the circumference of circle O is 16π inches. The length of is three-quarters of the

length of diameter and inches. Calculate the area, in square inches, of trapezoid ABCD.

14) Find the number of square inches in the area of the shaded region of this square which is being intersected by two semicircles. Leave answer in terms of S .

15) A square dance floor is positioned in the center of a ballroom as shown in the following diagram. If the

diameter of the circular dance floor is 6’, and one side of the dance room is 18’, what is the area of the carpeted region? (round to the nearest tenth)

16) Bill wishes to replace the carpet in his living room and hallway with laminate flooring. A floor plan is shown.

(a) Find the total area of floor to be recovered. (b) Laminate flooring comes in boxes that contain 2.15m2 of material. How many boxes will Bill require? (c) One box costs $ 43.25. How much will the flooring cost?

17) Christine has a rectangular plot of land with length = 20 feet, and width = 10 feet. She wants to design a

flower garden in the shape of a circle with two semicircles at each end of the center circle, as shown in the accompanying diagram. She will fill in the shaded area with wood chips. If one bag of wood chips covers 5 square feet, how many bags must he buy?

18) If asphalt pavement costs $0.78 per square foot, determine, to the nearest cent, the cost of paving the shaded

circular road with center O, an outside radius of 50 feet, and an inner radius of 36 feet, as shown in the accompanying diagram.

19) Find the area of the shaded region, leave your answer in terms of S .

20) Find the area of the triangle whose vertices are (-2, -5), (6, -3), and (0, 3).

21) Approximate the area of a circle using an inscribed regular 6-sided polygon (hexagon). Each side of the

hexagon is 20 and the distance from the center of the circle to each side of the hexagon is 10 3 . Express your answer in simplest radical form.

22) Approximate the area of a circle using an inscribed regular 6-sided polygon (hexagon). Each side of the

hexagon is 8 and the distance from the center of the circle to each side of the hexagon is 34 . Express your answer in simplest radical form.

23) Line k is drawn so that it is perpendicular to two

distinct planes, P and R. What must be true about planes P and R?

a) Planes P and R are skew. b) Planes P and R are parallel. c) Planes P and R are perpendicular. d) Plane P intersects plane R but is not

perpendicular to plane R.

24) Point P is on line m. What is the total number of planes that are perpendicular to line m and pass through point P?

a) 1 c) 0 b) 2 d) infinite

25) Point P lies on line m. Point P is also included in distinct planes Q, R, S, and T. At most, how many of these planes could be perpendicular to line m?

a) 1 c) 3 b) 2 d) 4

26) Plane R is perpendicular to line k and plane D is perpendicular to line k. Which statement is correct?

a) Plane R is perpendicular to plane D. b) Plane R is parallel to plane D. c) Plane R intersects plane D. d) Plane R bisects plane D.

27) In three-dimensional space, two planes are parallel and a third plane intersects both of the parallel planes. The intersection of the planes is a

a) plane c) pair of parallel lines b) point d) pair of intersecting

lines 28) Plane A is parallel to plane B. Plane C

intersects plane A in line m and intersects plane B in line n. Lines m and n are

a) intersecting c) perpendicular b) parallel d) skew

29) A cube has a volume of 729 cubic units. Calculate the length of one side of the cube. 30) The volume of a cylinder is S600 in3. The height of the cylinder is 6 inches. Calculate the radius of the

cylinder to the nearest tenth of an inch. 31) Mrs. Claus is taking an art class. Her art project is to make a cone vase. If the vase has a volume of 157 in3,

and a diameter of 10 inches, what is the height to the nearest inch? 32) The base of a pyramid is a rectangle with a width of 8 cm and a length of 9 cm. Find, in centimeters, the

height of the pyramid if the volume is 264 cm3.

33) Two cylinders are shown to the right. The dimensions of one of them are labeled.

When each dimension of the smaller cylinder is changed by a scale factor of 3, the larger cylinder is created. Which is the closed volume of the larger cylinder?

34) The volume of a sphere is S348,12 in3. Calculate the radius of the sphere. 35) The volume of a cylinder is S375 . If the height of the cylinder is 15, find the radius of the cylinder. 36) A cone has a volume of S432 cm3 and a height of 9cm. Calculate the radius of the cone. 37) Given a sphere with a radius equal to 3inches, find the area of the great circle. Express your answer in terms

of S .

38) If a regular square pyramid has a volume of 384cm3 and an altitude equal to 8cm, find one side of the base. 39) If the volume of a cube is equal to 343 m3, what is the side length of the cube? 40) An oblique prism has a rectangular base that is . A hole in the prism is also the shape of an

oblique prism with a rectangular base that is wide and long, and the prism’s height is (as shown in the diagram). Find the volume of the remaining solid.

41) An oblique circular cylinder has height and volume . Find the radius of the circular base. 42) If the Volume of the cube is 64cm3, what is the volume of the oblique prism if it has been tilted at a 60o

angle?

It will have the same volume as the cube so it will be 64 cm^3

43) Jenny says that the two prisms DO NOT have the same volume because the cross sections are not the same. Renee disagrees; she says that it isn’t the same shape that has to be the same it is the area of the base and height. Renee thinks they have the same volume. Who is right and why?

44) A rectangular prism and a cylinder have the same height and the same volume. What is the length of the

side of the prisms square base? 45) Find the volume of the oblique prism or cylinder below:

a) b) 46) Find the volume of the following

a) b)

Renee is right because they have the same volume

47) The area of the base of a cone is 20 and the height is 5. Find the area of a cross-section that is distance 3 from the vertex.

48) The following pyramids have equal altitudes, and both bases are equal in area and are coplanar. Both pyramids’ cross-sections are also coplanar. If BC = 3 and B’C’ = 1.5, and the area of triangle XYZ is 9, what is the area of cross-section A’B’C’D’?

49) The base of a pyramid is a trapezoid. The trapezoidal bases have lengths of 6 and 8, and the trapezoid’s

height is 3. Find the area of the parallel slice that is half of the way from the vertex to the base.

50) Find the area of any cross-section for the following prisms and if necessary leave your answer in terms of S .

a) b)

51) Pyramid X is similar to Pyramid Y. If the scale factor of X to Y is 3:7, what is the ratio of the volumes?

52) The cones below are similar. What is the volume of the larger cone in terms of S ? 53) The ratio of the sides of two similar cubes is 3:4. The smaller cube has a volume of 729 m3. What is the

volume of the larger cube? 54) Find the volume of the following:

55) Seawater contains approximately 1.2 ounces of salt per liter on average. How many gallons of seawater, to the nearest tenth of a gallon, would contain 1 pound of salt?

56) Trees that are cut down and stripped of their branches for timber are approximately cylindrical. A timber

company specializes in a certain type of tree that has a typical diameter of 50 cm and a typical height of about 10 meters. The density of the wood is 380 kilograms per cubic meter, and the wood can be sold by mass at a rate of $4.75 per kilogram. Determine and state the minimum number of whole trees that must be sold to raise at least $50,000.

57) Find the volume of water needed to fill three fourths of the aquarium.