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Understanding Dimensions, Surface Area, and Volume of Similar Solids

This educational guide explores the properties of similar solids, focusing on how to find missing linear measures, surface area, and volume. It emphasizes the proportional relationships between corresponding measures of similar shapes, using examples such as cones, prisms, and pyramids. The guide provides step-by-step instructions for deriving values using proportionality and ratios. With practical exercises and problems, learners can gain mastery over calculating dimensions and measurements of various geometric solids, making this resource ideal for students and educators alike.

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Understanding Dimensions, Surface Area, and Volume of Similar Solids

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  1. Find dimensions, surface area, and volume of similar solids. • similar solids Main Idea/Vocabulary

  2. Find Missing Linear Measures These cones are similar. What is the radius of Cone A to the nearest tenth? Since the two cones are similar, the ratios of their corresponding linear measures are proportional. Words Variable Equation Example 1

  3. Find Missing Linear Measures Write the proportion. Find the cross products. Multiply. Divide each side by 12. Simplify. Answer: The radius of cone A is about 4.7 centimeters. Example 1

  4. A B C D Cone A Cone B The cones are similar. What is the radius of Cone B to the nearest tenth? A. 6.5 cm B. 7.0 cm C. 7.5 cm D. 8.0 cm Example 1

  5. KC

  6. The ratio of the measures of prism A to prism B is Find Surface Area of a Similar Solid These rectangular prisms are similar. Find the total surface area of Prism A. Example 2

  7. Find Surface Area of a Similar Solid Write a proportion. Substitute the known values. Let S represent the surface area. Simplify. Find the cross products. Divide each side by 4. Simplify. Answer: The surface area of prism A is 846 square inches. Example 2

  8. A B C D These square pyramids are similar. Find the total surface area of Pyramid A. A. 476 cm2 B. 528 cm2 C. 562 cm2 D. 640 cm2 Example 2

  9. Find Volume of a Similar Solid A triangular prism has a volume of 12 cm3. Suppose the dimensions are tripled. What is the volume of the new prism? A. 36 cm3B. 96 cm3C. 324 cm3D. 1,728 cm3 Read the Item Example 3

  10. Find Volume of a Similar Solid Solve the Item Example 3

  11. Find Volume of a Similar Solid Write a proportion. Substitute the known values. Let V represent the volume of the larger prism. Simplify. Find the cross products. Simplify. Answer: So, the volume of larger prism is 324 cubic centimeters. The answer is C. Example 3

  12. A B C D A hexagonal prism has a volume of 25 cubic inches. Suppose the dimensions are tripled. What is the volume of the new prism? A. 75 in3 B. 120 in3 C. 200 in3 D. 675 in3 Example 3

  13. A B C D (over Lesson 7-8) Thirteen inches is the measure of what part of the pyramid? A.surface area B.lateral area C.slant height D.angle Five Minute Check 1

  14. A B C D (over Lesson 7-8) Find the lateral area of the pyramid. Round to the nearest tenth if necessary. A.260 in2 B.360 in2 C.195 in2 D.140 in2 Five Minute Check 2

  15. A B C D (over Lesson 7-8) Find the total surface area of the pyramid. Round to the nearest tenth if necessary. A.33 in2 B.53 in2 C.260 in2 D.360 in2 Five Minute Check 3

  16. A B C D (over Lesson 7-8) For an art project, only the sides of the pyramid are to be painted. If 1 ounce of enamel paint covers about 280 square inches and 2 coats are to be applied, how much paint should students have on hand for each pyramid? A.1 oz B.2 oz C.3 oz D.4 oz Five Minute Check 4

  17. A B C D (over Lesson 7-8) What is the approximate surface area of the pyramid? A.20 m2 B.78 m2 C.127 m2 D.274 m2 Five Minute Check 5

  18. End of Custom Shows

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