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Mathematics

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The net of a composite space figure is shown below.

a. What figures make up the composite space figure?

b. What is the surface area of the composite space figure? Round your answer to the nearest square centimeter.

Jack and Maureen are opening an ice hotel. The structure and furniture are made out of ice. They must determine the weight of some of the ice furniture to decide the size of the crane needed to lift each piece into place. Maureen knows that ice weighs approximately 62.4 pounds per cubic foot. Find the approximate weight of each of the figures below.

a. The stage in the banquet hall measures 22 ft by 15 ft by 4 ft.

b. Two cylindrical pillars will flank the front door. Each cylinder has diameter 1 ft and height 9 ft.

c. A series of four spheres will decorate the reception area. The largest sphere has diameter 4 ft. Th e other three spheres have diameter 2 ft, 1 ft, and 1/2 ft.

I have attached the project questions and rubric which contains all the requirements to receive a passing grade

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11 To solve these problems, you will pull together many concepts and skills that you have studied about surface area and volume. Pull It All Together Visualization You can use a net to visualize a three-dimensional solid. Task 1 The net of a composite space figure is shown below. 5 cm 6 cm 4 cm a. What figures make up the composite space figure? b. What is the surface area of the composite space figure? Round your answer to the nearest square centimeter. Measurement You can use formulas to find the volumes of various solids. Task 2 Jack and Maureen are opening an ice hotel. The structure and furniture are made out of ice. They must determine the weight of some of the ice furniture to decide the size of the crane needed to lift each piece into place. Maureen knows that ice weighs approximately 62.4 pounds per cubic foot. Find the approximate weight of each of the figures below. a. The stage in the banquet hall measures 22 ft by 15 ft by 4 ft. b. Two cylindrical pillars will flank the front door. Each cylinder has diameter 1 ft and height 9 ft. c. A series of four spheres will decorate the reception area. The largest sphere has 1 diameter 4 ft. The other three spheres have diameter 2 ft, 1 ft, and 2 ft. 750 Chapter 11 Pull It All Together Copyright © 2011 Pearson Education, Inc. Unit 11 Project Rubric Task 1 Correctly identifies all figures that make up the composite figure 3 points Correctly calculates area of each figure that makes up the composite figure. 3 points Correctly finds surface area. 2 points Total 8 points Task 2 Calculates weight of stage 2 points Calculates weight of pillars 2 points Calculates weight of each sphere 8 points Total 12 points
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a. The composite space figure is made up of hexagonal pyramid put on top of a hexagonal prism
base.
1

1

b. 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 = 2 ∗ 𝑏𝑎𝑠𝑒 ∗ ℎ𝑒𝑖𝑔ℎ𝑡 = 2 ∗ 4 ∗ 5 = 10𝑐𝑚2

𝐴𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑙𝑒 = 𝑙𝑒𝑛𝑔𝑡ℎ ∗ 𝑤𝑖𝑑𝑡ℎ = 6 ∗ 4 = 24𝑐𝑚2
𝐴 𝑟𝑒𝑔𝑢𝑙𝑎𝑟 ℎ𝑒𝑥𝑎𝑔𝑜𝑛 𝑖𝑠 𝑐𝑜𝑚𝑝𝑟𝑖𝑠𝑒𝑑 𝑜𝑓 𝑠𝑖𝑥 𝑒𝑞𝑢𝑖𝑙𝑎𝑡𝑒𝑟𝑎𝑙 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒𝑠, 𝑠𝑜 𝑎𝑟𝑒𝑎 𝑜𝑓 ℎ𝑒𝑥𝑎𝑔𝑜𝑛
3√3
3√3
√3
= 6 ∗ ( ∗ (𝑠𝑖𝑑𝑒)2 ) =
∗ (𝑠𝑖𝑑𝑒)2 =
∗ (4)2 = 24√3𝑐𝑚2
4
2
2
𝑠𝑜, 𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 the composite space figure
= 6 ∗ (𝑎𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 ) + 6 ∗ (𝑎𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑙𝑒) + 𝑎𝑟𝑒𝑎 𝑜𝑓 ℎ𝑒𝑥𝑎𝑔𝑜𝑛
= (6 ∗ 10) + (6 ∗ 24) + 24√3 𝑐𝑚2 = 60 + 144 + 41.57 𝑐𝑚2 = 245.57 𝑐𝑚2
𝑹𝒐𝒖𝒏𝒅𝒊𝒏𝒈 𝒕𝒉𝒆 𝒂𝒏𝒔𝒘𝒆𝒓 𝒕𝒐 𝒕𝒉𝒆 𝒏𝒆𝒂𝒓𝒆𝒔𝒕 𝒔𝒒𝒖𝒂𝒓𝒆 𝒄𝒆𝒏𝒕𝒊𝒎𝒆𝒕𝒆𝒓:
𝑺𝒖𝒓𝒇𝒂𝒄𝒆 𝒂𝒓𝒆𝒂 𝒐𝒇 𝐭𝐡𝐞 𝐜𝐨𝐦𝐩𝐨𝐬𝐢𝐭𝐞 𝐬𝐩𝐚𝐜𝐞 𝐟𝐢𝐠𝐮𝐫𝐞 𝐢𝐬 𝟐𝟒𝟔 𝐜𝐦𝟐

a. �...

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