Chapter Ten: Area (10-1) (10-2) (10-3)

WORD BANK:

altitude

area

prism

pyramid

cylinder

cone

sphere

net

surface area

volume

An ______is a line segment perpendicular to the line containing the base of the figure and drawn from the side opposite that base. The altitude is the height of the figure.

The ______of a figure is the number of square units it encloses.

The area of a parallelogram is: A = bh

The area of a triangle is: A = ½ bh

The area of a trapezoid is: A = ½ (sum of the bases) * h

The area of a circle is: A = pr 2

The following problems are copied from Prentice Hall Pre-Algebra:

Practice: (p. 525+ ) Find the area of each shaded region.

#22)

#11) A triangle and a parallelogram both have areas of 20 cm2 and bases of 5 cm. How do their heights compare?

#13) A trapezoid has area 50 in2. The two bases are 5 in. and 15 in. What is the height of the trapezoid?

Answers: 22) 20.16 m2; 11) The triangle’s height must be twice that of the parallelogram because it’s ½*b*h.; 13) The height of the trapezoid must be 5 in. because it’s ½* base 1 + base 2 * h.

Chapter Ten: Area (10-1) (10-2) (10-3)

Practice: (pp.530+531)

#14) Sketch and label two different triangles so that both have areas of 180 cm2.

#23) A right trapezoid has sides 24.5 mm, 17.5mm, 14mm, and 14mm. What is the perimeter? What is the area? Draw the trapezoid.

Practice: (pp. 536+537)

#23) Which has a greater area, four circles, each with radius 1 m, or one circle with radius 4m? Explain your reasoning.

Answers: 23) The perimeter is 70 mm; p. 536: 23) The circle with a radius of 4 m is larger. It has an area of 50.24 m2 while the circles with radii of 1m are each only 3.14 m2 for a total of 12.56 m2.

Chapter Ten: Area (10-1) (10-2) (10-3)

Practice: (pp. 535-537)

#24) How many circles with radius 2 cm will have the same total area as a circle with radius 4 cm? Explain your reasoning.

#29a) A manufacturer cuts lids for eight cans from one rectangular sheet of aluminum. What is the radius of each lid?

b) How many square inches of aluminum do the lids require?

c) How many square inches of aluminum are wasted?

#30a) You can buy a 10-in. diameter pizza for $6.50, a 12-in. pizza for $8.50, and or a 14-in. pizza for $10.50. What is the area of each pizza to the nearest square inch?

b) What is the price per square inch of each pizza?

c) Is the largest pizza the best buy? Explain.

Answers: 24) 4 circles of 2 cm = one circle of 4 cm [ 22 is 4, while 42 is 16: 4 times as much]; 29a) each lid r= 3in; b)area of lids= 226.08 in2; c) 61.92 in2 are wasted; 30a) area of 10-in =78.50 in2, area of 12-in= 113.04 in2, area of 14-in = 153.86 in2. b) price per square inch for: 10-in = $.082, 12-in = $.075, 14-in = $.068. c) Yes. The largest pizza is the best buy.

Chapter Ten: Surface Area (10-4) (10-5) (10-6)

3-D Figures:

A ______has two parallel bases that are congruent polygons, and lateral faces that are parallelograms. A ______has a base that is a polygon and lateral faces that are triangles. A ______has two parallel bases that are congruent circles. A ______has one circular base and one vertex. A ______is the set of all points in space that are equidistance from a center. A ______is a pattern you can form into a 3-D figure.

Surface area (S.A.)

______is the sum of the areas of the base(s) and the lateral faces of a 3-D figure. One way to find the surface area is to find the area of its net.

The surface area of a prism is: S.A.= L.A. + 2B; where L.A. is the surface area of its lateral faces, and B is the area of one of its congruent bases.

The surface area of a cylinder is: S.A.= L.A. + 2B; where L.A. = 2 prh and B = pr 2

The lateral area of a pyramid is ½ the product of the perimeter of the base and the slant height. The surface area of a pyramid is the sum of the lateral are and the area of the base.

L.A. = ½ pl S.A. = L.A. + B

The surface area of a cone is the sum of the lateral are and the area of the base.

L.A. = prl S.A. = L.A. + B

The surface area of a sphere of radius r is: S.A. = 4 pr 2

Practice: (pp. 542+549)

#24) How are the nets of a rectangular prism and a rectangular pyramid similar, and how are they different?

#32) A rectangular prism has how many faces?

#13) Juliet is trying to wrap a can of mixed nuts that is a birthday gift for her brother. The can has a radius of 8cm and a height of 10 cm. Approximately how many square centimeters of wrapping paper will cover the gift?

Answers: 24) Pyramids have lateral faces that are triangular while prisms do not. 32) 6 faces; 13) 351.68 cm2

Chapter Ten: Surface Area (10-4) (10-5) (10-6)

Practice: (pp. 542+549)

#17) A tent is approximately the shape of a triangular prism. Its base is 44 in by 72 in. Its height is 36 in. The ends of the tent are isosceles triangles with 42 in congruent sides. Approximate the area of the tent, including the bottom, by finding the surface area of the prism.

#19b) The neighborhood pool needs to be painted. It is 40 ft. by 60 ft. It is 6 ft deep throughout. What is the total number of square feet to be painted?

c) The materials for painting the pool cost $1.50 per square yard. What is the cost of the materials for painting the pool?

#23) You have made two boxes with lids. Which box required more cardboard, a box 8 in. by 6.25 in. by 10.5 in. or a box by 9 in. by 5.5 in. by 11.75 in.? Explain.

#24) Write a rule for the surface area of cubes: 1 by 1; 2 by 2; 3 by 3; … If the length is tripled, how does that affect the surface area? Why?

Answers: 17) 10,800 in2; 19b) 3600 ft2; c) $5,400; 23) 9 by 5.5 by 11.75 is larger than 8 by 6.25 by 10.5; the first is 439.75 in2, while the second is 416.05 in2. let t= the term number, t2 * 6 = the total surface area

Chapter Ten: Volume (10-7) (10-9)

The ______of a 3-D figure is the number of cubic units needed to fill it. A cubic unit is a cube with edges one unit long.

The volume of a prism is: V= Bh

where B= the area of its base

The volume of a cylinder is: V= Bh

where B= the area of its base

The volume of a pyramid is: V= 1/3 Bh

where B= the area of its base

The volume of a sphere is: V = 4/3 pr 3

Practice: (p. 555)

#14) A friend tells you that the surface area of a square prism with base length 4 m and height 5 m is the same as the surface area of a square pyramid with base length 4 m and height 5 m. Explain your friend’s error and find the volume of each.

p. 559) Find the volume of the following:

#7a) a mailing tube 25 in. long with a diameter of 4 in.

b) a mailing tube with double the dimensions in part (a)

c) How do the volumes of the two mailing tubes compare?

#17) Concrete is sold by the yard, which means by the cubic yard. It costs $70 per yard. How many cubic feet are in a cubic yard? How much would it cost to pour a slab that is 14 ft by 16 ft by 6 in. for a patio?

Answers: 14) The SA of the prism is 112 m2, while the SA of the pyramid is 56 m2; 7a) 314 in3; b) 2,512 in3; c) 8 times as big; 17) There are 27 cubic feet in one cubic yard. 112 feet3 would cost $7,840