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3D Geometry Flashcards

3D Geometry Flashcards
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Find the volume of the pyramid.

Volume of a pyramid = (B * h) / 3
B = 4 * 4 = 16 meters squared
h = 7 m
Volume = 16 meters squared * 7 meters = 112 meters
112 / 3 = 37.33

Got it
Find the surface area of the pyramid.
Surface area of a pyramid = B + (P *s)/2
B = 4 * 4 = 16 meters squared
P = 4 + 4 + 4 + 4 = 16 m
s = 9 m
Surface area = 16 + (16 * 9)/2 = 16 + 72 = 88 meters squared
Got it
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
Got it
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
Got it
Volume of the pictured triangular prism
Volume of a prism = B * h
B = 1/2 * 6 * 3 = 9 meters squared
Volume = 9 meters squared * 10 m = 90 meters cubed
Got it
Surface area of this rectangular prism
Surface area of a prism = 2 * B + P * h
B = 3 * 4 = 12 meters squared
P = 4 + 3 + 4 + 3 = 14 m
h = 9 m
Surface area = 2 * 12 + 14 * 9 = 24 + 126 = 150 meters squared
Got it
Formula for the volume of a prism
Volume of a prism = B * h
B is the area of the base
h is the height
Got it
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
Got it
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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19 cards in set

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.

Front
Back
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 height
Formula for the volume of a prism
Volume of a prism = B * h
B is the area of the base
h is the height
Surface area of this rectangular prism
Surface area of a prism = 2 * B + P * h
B = 3 * 4 = 12 meters squared
P = 4 + 3 + 4 + 3 = 14 m
h = 9 m
Surface area = 2 * 12 + 14 * 9 = 24 + 126 = 150 meters squared
Volume of the pictured triangular prism
Volume of a prism = B * h
B = 1/2 * 6 * 3 = 9 meters squared
Volume = 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 height
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
Find the surface area of the pyramid.
Surface area of a pyramid = B + (P *s)/2
B = 4 * 4 = 16 meters squared
P = 4 + 4 + 4 + 4 = 16 m
s = 9 m
Surface area = 16 + (16 * 9)/2 = 16 + 72 = 88 meters squared
Find the volume of the pyramid.

Volume of a pyramid = (B * h) / 3
B = 4 * 4 = 16 meters squared
h = 7 m
Volume = 16 meters squared * 7 meters = 112 meters
112 / 3 = 37.33

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 * 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 * 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 = (πr 2h)/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 2
Formula for the volume of a sphere
Volume of a sphere = (4/3) * π * r 3
Surface area of a sphere with a radius of 4 inches
Surface area of a sphere = 4 * π * 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 * r 3
= (4/3) * 3.14 * 23
= (4/3) * 3.14 * 8
= 33.49 inches cubed

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