Chapter 12 – Extending Surface Area and Volume

Section 2 – Surface Areas of Prisms and Cylinders

  • I can apply geometric methods to solve design problems.
  • I can find the surface area of prisms, cylinders, pyramids, spheres and cones.
  • I can describe the difference between lateral and surface area.
  • Lateral Areas and Surface Areas of Prisms – In a solid figure, faces that are NOT bases are called lateral faces. Lateral faces intersect the bases at the base edges. The altitude is a perpendicular segment that joins the planes of the bases and the altitude represents the height of the figure.

  • Lateral Area = Perimeter times height (L = Ph)
  • Surface Area = Lateral Area (Perimeter*height) + 2 times base (S = Ph + 2B)
  1. Find the lateral area of the regular hexagonal prism.

*Guided Practice #1. The length of each side of the base of a regular octagonal prism is 6 inches, and the height is 11 inches. Find the lateral area.

  1. Find the surface area of the rectangular or triangular prism.

(a)(b)

  • Lateral Areas and Surface Areas of Cylinders

  • Lateral Area = 2 Pi times radius times height (L = 2 rh)
  • Surface Area = Lateral Area (2Pi times radius times height) + 2 Pi times radius squared

(S = 2 rh + 2 r2)

  1. Find the lateral area and the surface area of the cylinder. Round to the nearest tenth.

*Guided Practice #3. Find the lateral and surface area of the cylinders to the nearest tenth.

3A. r = 5 in., h = 9 in.3B. d = 6 cm, h = 4.8 cm

4. A soup can is covered with the label shown. What is the radius of the soup can?

Guided Practice #4: Find the diameter of a base of a cylinder if the surface area is 464 square centimeters an the height is 21 centimeters.

Homework – Page 834 – 836 (9 – 23) ODD (24, 25, 26, 27, 30, 31, 39)ALL

Section 4 – Volumes of Prisms and Cylinders

  • I can define as the ratio of a circle’s circumference to its diameter.
  • I can use algebra to demonstrate that because is the ratio of a circle’s circumference to its diameter that the formula for a circle’s circumference must be C = ?d.
  • I can develop formulas to calculate the volumes of 3-D figures including spheres, cones, prisms, and pyramids.
  • I can apply geometric methods to solve design problems.
  • I can apply the concept of density when referring to situations involving area and volume.
  • Volume of a Prism – Volume = area of the Base times the height of the figure (V = Bh)
  • Volume of a Cylinder – Volume = Pi times radius squared times height (V = r2 h)
  1. Find the volume of the prism.
  1. Find the volume of the cylinder. Round to the nearest tenth.
  1. Find the volume of an oblique cylinder. Round to the nearest tenth.

Guided Practice #3: Find the volume of an oblique cylinder that has a radius of 5 feet and a height of 3 feet. Round to the nearest tenth.

  1. Prisms A and B have the same width and height, but different lengths. If the volume of Prism B is 128 cubic inches greater than volume A, what is the length of each prism?

Homework – Page 850 – 853 (10 – 19, 21, 32, 33, 42)ALL

Section 3 – Surface Areas of Pyramids and Cones

  • I can use geometric shapes, their measures and their properties to describe objects.
  • I can find the surface area of prisms, cylinders, pyramids, spheres and cones.
  • I can describe the difference between lateral and surface area.
  • Lateral Area of a Pyramid – L = ½ Pl (P=perimeter of the base and l = the slanted height)
  • Surface Area of a Pyramid - S = ½ Pl + B (lateral area + 2 times the area of the base)
  1. Find the lateral area of the square pyramid.

Guided Practice #1: Find the lateral area of a regular hexagonal pyramid with a base edge of 9 centimeters and a lateral height of 7 centimeters.

  1. Find the surface area of the square pyramid to the nearest tenth.
  1. Find the surface area of the regular pyramid. Round to the nearest tenth.
  • Lateral Area of a Cone – L = rl (r = radius and l = slanted height)
  • Surface Area of a Cone – S = rl + r2
  1. A sugar cone has an altitude of 8 inches and a diameter of 2.5 inches. Find the lateral area of the sugar cone.

Guided Practice #4: A waffle cone is 5.5 inches tall and the diameter of the base is 2.5 inches. Find the lateral area of the cone and round to the nearest tenth.

  1. Find the surface area of the cone. Round to the nearest tenth.

Guided Practice #5: Find the surface area of the cone.

A.B.

Homework – Page 843-844 (7-11, 13-15, 17, 23, 24, 25, 26, 27, 33, 34)

Section 5 – Volumes of Pyramids and Cones

  • I can define as the ratio of a circle’s circumference to its diameter.
  • I can use algebra to demonstrate that because is the ratio of a circle’s circumference to its diameter that the formula for a circle’s circumference must be C = ?d.
  • I can develop formulas to calculate the volumes of 3-D figures including spheres, cones, prisms, and pyramids.
  • I can apply geometric methods to solve design problems.
  • I can apply the concept of density when referring to situations involving area and volume.
  • Volume of a Pyramid – 1/3 Bh (B= area of the base and h = height)
  • Volume of a Cone - 1/3 r2h
  1. Find the volume of the pyramid.
  1. Find the volume of each cone. Round to the nearest tenth.

(a)(a)(b)

  1. At the top of a stone tower is a pyramidion in the shape of a square pyramid. This pyramid has a height of 52.5 centimeters and the base edges are 36 centimeters. What is the volume of the pyramidion? Round to the nearest tenth.

Homework – Page 860-862 (10 – 13, 16 – 20, 23, 24, 27, 28, 32, 33, 37)ALL

Section 6 – Surface Areas and Volumes of a Sphere

  • I can define as the ratio of a circle’s circumference to its diameter.
  • I can use algebra to demonstrate that because is the ratio of a circle’s circumference to its diameter that the formula for a circle’s circumference must be C = ?d.
  • I can develop formulas to calculate the volumes of 3-D figures including spheres, cones, prisms, and pyramids.
  • I can apply geometric methods to solve design problems.
  • Surface Area of a Sphere – S = 4r2
  • Surface Area of a Hemisphere (half a sphere) - 3 r2
  1. Find the surface area of the sphere. Round to the nearest tenth.

2. (a) Find the surface area of the hemisphere.

(b) Find the surface area of a sphere if the circumference of the great circle is 10 feet.

( c) Find the surface area of a sphere if the area of the great circle is approximately 220 square meters.

  • Volume of a Sphere – 4/3 r3
  • Volume of a Hemisphere – ½ (4/3 r3) OR (2/3 r3 )
  1. Find the volume of each sphere or hemisphere. Round to the nearest tenth.

(a) a sphere with a great circle circumference of 30centimeters.

(b) a hemisphere with a diameter of 6 feet

Guided Practice: Find the volume of each:

3A. Sphere: diameter = 7.4 in.

3B. Hemisphere: area of great circle = 249mm

4. The stone spheres of Costa Rica were made by forming granodiorite boulders into spheres. One of the stone spheres has a volume of about 36,000 cubic inches. What is the diameter of the stone sphere?

Homework – Page 868 – 869 (10 – 27, 29, 30, 31) ODD

Section 8 – Congruent and Similar Solids

  • I can use the similarity ratio between two solids to find the volume.
  • I can use geometric shapes, their measures and their properties to describe objects.

Page 880 has formulas for these. They will be ratios!

  1. Determine whether each pair of solids is similar, congruent, or neither. If the solids are similar, state the scale factor.

Guided Practice: Determine if each pair is similar, congruent or neither. If similar, state the scale factor.

1A.

1B.

  1. Two similar cones have radii of 9 inches and 12 inches. What is the ratio of the volume of the smaller cone to the volume of the larger cone?

Guided Practice #2: Two similar prisms have surface areas of 98 square centimeters and 18 square centimeters. What is the ratio of the height of the large prism to the height of the small prism?

  1. The softballs below are similar spheres. If the radius of the larger softball is 1.9 inches, find the radius of the smaller softball.

Guided Practice #3: A regulation volleyball has a circumference of about 66cm. The ratio of the surface area of that ball to the surface area of a children’s ball is approximately 1.6:1. What is the circumference of the children’s ball? Round to the nearest centimeter.

Homework – Page 883-885 (6-16, 21, 27)ALL