Circumference, Area, and Volume Chapter 11

Area of Polygons I can find the area of rhombuses, kites, and regular polygons.

Area of Polygons Vocabulary (page 326 in Student Journal) apothem of a regular polygon: the distance from the center to any side of a regular polygon

Area of Polygons Core Concepts (pages 274, 326 and 327 in Student Journal) Area of a Triangle A = ½ bc(sin A)

Area of Polygons Area of a Rhombus or Kite A = ½ d1d2, where d1 and d2 are the lengths of the diagonals.

Area of Polygons Area of a Regular Polygon A = ½ aP, where a is the length of the apothem and P is the perimeter.

Area of Polygons Examples (space on pages274, 326 and 327 in Student Journal) a) Find the area.

Area of Polygons Solutions a) 84.6 square units

Area of Polygons Find the area. b) c)

Area of Polygons Solutions b) 27.5 square feet c) 120 square millimeters

Area of Polygons Find the area. d) e)

Area of Polygons Solutions d) 665.11 square units e) 222.5 square inches

Surface Area I can find the surface area of cones and spheres.

Surface Area Vocabulary (page 346 in Student Journal) lateral surface of a cone: all segments that connect the vertex with points on the base edge

Surface Area Core Concepts (page 346 and 351 in Student Journal) Surface Area of a Right Cone S = πr2 + πrl, where r is the radius and l is the slant height Surface Area of a Sphere S = 4πr2, where r is the radius

Surface Area Examples (space on pages 346 and 351 in Student Journal) Find the surface area. a) b)

Surface Area Solutions a) 282.74 square inches b) 28.27 square feet

Volume I can find volumes of prisms, cylinders, pyramids, cones, and spheres.

Volume Vocabulary (pages 336 and 341 in Student Journal) Cavalieri’s Principle: if 2 solids have the same height and the same cross-sectional area at every level, then they have the same volume composite solid: a solid that is made up of 2 or more solids

Volume Core Concepts (pages 336, 337, 341, 347, and 352 in Student Journal) Volume of a Prism and Cylinder V = Bh, where B is the area of the base and h is the height

Volume Volume of a Pyramid and Cone V = 1/3Bh, where B is the area of the base and h is the height Volume of a Sphere V = 4/3πr3

Volume Examples (space on pages 336, 337, 341, 347, and 352 in Student Journal) Find the volume. a) b)

Volume Solutions 52.5 cubic meters 3386.64 cubic feet

Volume Find the volume. c) d)

Volume Solutions c) 12.8 cubic meters d) 1680 cubic meters

Volume Find the volume. e) f)

Volume Solutions e) 879.65 cubic meters f) 14.14 cubic feet

Circumference and Arc Length I can use the formula for circumference and use arc lengths to find measures.

Circumference and Arc Length Vocabulary (page 316 in Student Journal) circumference: the distance around the circle arc length: a portion of the circumference of a circle radian: a unit of measurement for angles, which uses the length of the arc of the corresponding central angle to describe the amount of rotation

Circumference and Arc Length Core Concepts (pages 316 and 317 in Student Journal) Circumference of a Circle C = 2πr Arc Length arc length = 2πr(measure of arc/360)

Circumference and Arc Length Converting between Degrees and Radians Degree to radians: multiply degree by 2π/360 Radian to degree: multiply radian by 360/2π

Circumference and Arc Length Examples (space on pages 316 and 317 in Student Journal) Find the indicated measure. circumference of a circle with a radius of 11 inches radius of a circle with a circumference of 4 millimeters

Circumference and Arc Length Solutions 69.12 inches 0.64 millimeters

Circumference and Arc Length Find the indicated measure in the diagram. c) arc length of arc PR d) circumference of circle P e) measure of arc JK

Circumference and Arc Length Solutions c) 20.94 inches d) 18 meters e) 84 degrees

Circumference and Arc Length f) Convert 30 degrees to radians. g) Convert 3π/8 radians to degrees.

Circumference and Arc Length Solutions f) π/6 radians g) 67.5 degrees

Areas of Circles and Sectors I can use the formula for the area of a circle and find areas of sectors.

Areas of Circles and Sectors Vocabulary (page 321 in Student Journal) sector of a circle: the region bounded by 2 radii of a circle and their intercepted arc

Areas of Circles and Sectors Core Concepts (pages 321 and 322 in Student Journal) Area of a Circle A = πr2 Area of a Sector area of sector = πr2(measure of arc)/360

Areas of Circles and Sectors Examples (space on pages 321 and 322 in Student Journal) Find the indicated measure. area of a circle with a radius of 8.5 inches diameter of a circle with an area of 153.94 feet squared

Areas of Circles and Sectors Solutions 226.98 inches2 14 feet

Areas of Circles and Sectors Find the indicated area. c) area of the blue sector d) area circle S

Areas of Circles and Sectors Solutions c) 441.79 square centimeters d) 128 square feet