Three dimensional geometry/Measurement
Mathematics, Grade 8
Three dimensional geometry/Measurement
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Three dimensional geometry/Measurement
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Three dimensional geometry/Measurement
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Three dimensional geometry/Measurement
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Three dimensional geometry/Measurement
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Study Guide Three dimensional geometry/Measurement Mathematics, Grade 8
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THREE-DIMENSIONAL GEOMETRY/ MEASUREMENT Three-dimensional geometry/measurement refers to three-dimensional (3- D) shapes and the measurement of their shapes concerning volume and surface area. The figures of prisms, cylinders, pyramids, cones and spheres are all 3-D figures. Volume measures the amount a solid figure can hold. Volume is measured in terms of units³ and can be measured in inches, feet, meters, centimeters, and millimeters. • The volume of a rectangular prism is V = l · w · h , where l is the length, w is the width, and h is the height. • The volume of a cube is V = s³, where s is a side of the square. • The volume of a triangular prism is V = B · h , where B is 1/2 · b · h. • The volume of a cylinder is V = π r² · h, where r is the radius and h is the height. Pi (π) is approximately 3.14. • The volume of a pyramid is V = (1/3) b² · h , where b is the side of the base and h is the height of the pyramid. • The volume of a cone is V = (1/3)π r² · h, where r is the radius and h is the height. • The volume of a sphere is V = (4/3)π r³, where r is the radius and π is 3.14. Surface area is the sum of the areas of all the surfaces of an object. • The surface area of a rectangular prism is: SA = 2wl + 2lh + 2 hw. • The surface area of a triangular prism is: SA = bh + (a + b + c)h, where bh refers to base times height and a, b and c are the sides of a triangle and h is the height. • The surface area of a cylinder is: SA = 2π r · h + 2π r², where r is the radius and h is the height. • The surface area of a square pyramid is: SA = s² + 2sl, where s is a base side and l is the slant height. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
• The surface area of a cone is: SA = πr(r + s), where r is the radius and s is the slant height. • The surface area of a sphere is: SA = 4π r². How to use 3-D geometry/measurement The volume of 3-D figures can be determined by using the formula that corresponds to the figure. The volumes of all figures can be determined as long as the needed information is given. For example, what is the volume of a cone with a radius of 6 cm and a height of 15 cm? The number 3.14 is used for π. Ex. Vcone = (1/3)π r² · h = (1/3)(3.14)(6²)(15) Vcone = (1/3)(3.14)(36)(15) = 565.2 cm³ If the volume of a figure is given, as well as the information needed to solve for volume except one value, the missing value can be found by substituting in all the given information and solving. Surface area is the sum of all the areas of the surfaces of an object. The surface area of any figure can be found using the appropriate formulas. For example, what is the surface area of a sphere with a radius of 5 inches? Ex. SA sphere = 4π r² = (4)(3.14)(5²) = (4)(3.14)(25) = 314 inches If the surface area and all other dimensions are given except one dimension, the missing dimension can be found by plugging in the surface area and given dimensions and solving for the missing dimension. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
Try This! 1. What is the volume of the rectangular prism with a length of 4m, a width of 6 m and a height of 12 m? V = l · w · h 2. What is the volume of a triangular prism with a length of 9 cm, a width of 10 cm and a height of 3 cm? V = (1/2) · l · w · h 3. What is the volume of a pyramid with a height of 15 cm and a base of 8 cm? V = (1/3) b² · h 4. If the volume of a cylinder is 1230.88 m³ and the radius is 7 m, what is the height? V = π r² · h 5. If the volume of a cone is 1780.38 in.³ and the radius is 9 in., what is the height? V = (1/3)π r² · h 6. If the volume of a sphere is 113.04ft, what is the radius? V = (4/3)π r³ 7. What is the surface area of a rectangle with a length of 4 cm, a width of 7 cm and a height of 11 cm? 8. What is the surface area of a cylinder with a radius of 14 in. and a height of 30 in.? 9. What is the surface area of a sphere with a diameter of 16 ft? © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
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