# 3D Geometry Flashcards

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Find the volume of the pyramid.

Volume of a pyramid = (

Volume = 16 meters squared * 7 meters = 112 meters cubed

*B***h*)/3*B*= 4 * 4 = 16 meters squared*h*= 7 mVolume = 16 meters squared * 7 meters = 112 meters cubed

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Find the surface area of the pyramid.

Surface area of a pyramid =

Surface area = 16 + (16 * 9)/2 = 16 + 72 = 88 meters squared

*B*+ (*P***s*)/2*B*= 4 * 4 = 16 meters squared*P*= 4 + 4 + 4 + 4 = 16 m*s*= 9 mSurface area = 16 + (16 * 9)/2 = 16 + 72 = 88 meters squared

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Formula for the volume of a pyramid

Volume of a pyramid = (

*B***h*)/3*B*is the area of the base*h*is the height
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Formula for the surface area of a pyramid

Surface area of a pyramid =

*B*+ (*P***s*)/2*B*is the area of the base*P*is the perimeter of the base*s*is the slant height
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Volume of the pictured triangular prism

Volume of a prism =

Volume = 9 meters squared * 10 m = 90 meters cubed

*B * h**B*= 1/2 * 6 * 3 = 9 meters squaredVolume = 9 meters squared * 10 m = 90 meters cubed

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Surface area of this rectangular prism

Surface area of a prism = 2 *

Surface area = 2 * 12 + 14 * 9 = 24 + 126 = 150 meters squared

*B*+*P***h**B*= 3 * 4 = 12 meters squared*P*= 4 + 3 + 4 + 3 = 14 m*h*= 9 mSurface area = 2 * 12 + 14 * 9 = 24 + 126 = 150 meters squared

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Formula for the volume of a prism

Volume of a prism =

*B***h**B*is the area of the base*h*is the height
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Formula for the surface area of a prism

Surface area of a prism = 2 *

*B*+*P***h**B*is the area of the base*P*is the perimeter*h*is the height
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Define the term: Platonic Solid

Any three-dimensional shape where each face is the same polygon and each vertex (or corner) is the meeting point for the same number of polygons.

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## Flashcard Content Overview

This flashcard set covers a wide array of 3D shapes. It includes practice learning the formulas for the surface area and volume of shapes, such as pyramids, cones, spheres, cylinders and prisms. It also includes practice problem flashcards for each of these shapes.

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Define the term: Platonic Solid

Any three-dimensional shape where each face is the same polygon and each vertex (or corner) is the meeting point for the same number of polygons.

Formula for the surface area of a prism

Surface area of a prism = 2 *

*B*+*P***h**B*is the area of the base*P*is the perimeter*h*is the heightFormula for the volume of a prism

Volume of a prism =

*B***h**B*is the area of the base*h*is the heightSurface area of this rectangular prism

Surface area of a prism = 2 *

Surface area = 2 * 12 + 14 * 9 = 24 + 126 = 150 meters squared

*B*+*P***h**B*= 3 * 4 = 12 meters squared*P*= 4 + 3 + 4 + 3 = 14 m*h*= 9 mSurface area = 2 * 12 + 14 * 9 = 24 + 126 = 150 meters squared

Volume of the pictured triangular prism

Volume of a prism =

Volume = 9 meters squared * 10 m = 90 meters cubed

*B * h**B*= 1/2 * 6 * 3 = 9 meters squaredVolume = 9 meters squared * 10 m = 90 meters cubed

Formula for the surface area of a pyramid

Surface area of a pyramid =

*B*+ (*P***s*)/2*B*is the area of the base*P*is the perimeter of the base*s*is the slant heightFormula for the volume of a pyramid

Volume of a pyramid = (

*B***h*)/3*B*is the area of the base*h*is the heightFind the surface area of the pyramid.

Surface area of a pyramid =

Surface area = 16 + (16 * 9)/2 = 16 + 72 = 88 meters squared

*B*+ (*P***s*)/2*B*= 4 * 4 = 16 meters squared*P*= 4 + 4 + 4 + 4 = 16 m*s*= 9 mSurface area = 16 + (16 * 9)/2 = 16 + 72 = 88 meters squared

Find the volume of the pyramid.

Volume of a pyramid = (

Volume = 16 meters squared * 7 meters = 112 meters cubed

*B***h*)/3*B*= 4 * 4 = 16 meters squared*h*= 7 mVolume = 16 meters squared * 7 meters = 112 meters cubed

Formula for the surface area of a cylinder

Surface area of a cylinder = 2 * π *

*r** (*r*+*h*)Formula for the volume of a cylinder

Volume of a cylinder = π *

*r*2 **h*Find the surface area of this cylinder

Surface area of a cylinder = 2 * π *

= 2 * 3.14 * 3 * (3 + 5)

= 150.72 meters squared

*r** (*r*+*h*)= 2 * 3.14 * 3 * (3 + 5)

= 150.72 meters squared

Find the volume of the pictured cylinder

Volume of a cylinder = π *

= 3.14 * 32 * 5

= 141.3 meters cubed

*r*2 **h*= 3.14 * 32 * 5

= 141.3 meters cubed

Formula for the volume of a cone

Volume of a cone =

Find the volume of a cone with a radius of 2 m and a height of 5 m.

Volume of a cone = (π

= (3.14 * 22 * 5)/3

= (3.14 * 4 * 5)/3

= 62.8/3

= 20.93 meters cubed

*r*2*h*)/3= (3.14 * 22 * 5)/3

= (3.14 * 4 * 5)/3

= 62.8/3

= 20.93 meters cubed

Formula for the surface area of a sphere

Surface area of a sphere = 4 * π *

*r*2Formula for the volume of a sphere

Volume of a sphere = (4/3) * π *

*r*3Surface area of a sphere with a radius of 4 inches

Surface area of a sphere = 4 * π *

= 4 * 3.14 * 42

= 4 * 3.14 * 16

= 200.96 inches squared

*r*2= 4 * 3.14 * 42

= 4 * 3.14 * 16

= 200.96 inches squared

Volume of a sphere with a radius of 2 inches

Volume of a sphere = (4/3) * π *

= (4/3) * 3.14 * 23

= (4/3) * 3.14 * 8

= 33.49 inches cubed

*r*3= (4/3) * 3.14 * 23

= (4/3) * 3.14 * 8

= 33.49 inches cubed

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Lesson
13 in chapter 16 of the course:

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Geometry 101: Intro to Geometry16 chapters | 145 lessons | 12 flashcard sets

- Solving Line & Angle Problems in Geometry: Practice Problems
- Practice with Shapes in Geometry: Practice Problems
- Basics of Geometry Flashcards
- Logic & Proof in Mathematics Flashcards
- Intro to Geometric Figures Flashcards
- Triangle Properties & Construction Flashcards
- Parallel Lines & Polygons Flashcards
- Triangle Congruence, Ratios & Proportions Flashcards
- Similar Polygons Flashcards
- Quadrilaterals Overview Flashcards
- Circles Overview Flashcards
- Conic Sections Overview Flashcards
- 3D Geometry Flashcards
- Go to Studying for Geometry 101

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