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solids shapes

Author:Sans, alyssamilan, azb, Sharyn, Lepressley, Freyja Fallson-Ree, GeoGebra Materials Team, Mathguru
Topic:Volume

Cube

A cube is a three-dimensional shape that has six square faces. All edges of a cube have the same length, and all angles are right angles. Examples of cube-shaped objects include dice, Rubik’s cubes, and ice cubes. Elements of a Cube A cube has several important parts: Faces: A cube has 6 square faces. Edges: A cube has 12 edges with equal lengths. Vertices: A cube has 8 vertices or corner points. Face Diagonals: A cube has 12 face diagonals. Space Diagonals: A cube has 4 space diagonals. Diagonal Planes: A cube has 6 diagonal planes. A cube net is a two-dimensional pattern that can be folded to form a cube. There are many different cube net patterns, but not all arrangements of squares can form a cube. The surface area of a cube is the total area of all six square faces.

Formula: Surface Area = Formula: Volume = Diagonals of a Cube: Face Diagonal A face diagonal is a line connecting two opposite corners on the same face of the cube. Formula: Face Diagonal = Space Diagonal A space diagonal is a line connecting two opposite vertices through the inside of the cube. Formula: Space Diagonal =

Net of a Cube

Definition of a Cuboid

A cuboid is a three-dimensional shape that has three pairs of rectangular faces. The opposite faces have the same size and shape. Examples of cuboid-shaped objects include boxes, bricks, cupboards, and aquariums. Elements of a Cuboid Faces A cuboid has 6 rectangular faces. Edges A cuboid has 12 edges. Vertices A cuboid has 8 vertices. Face Diagonals A cuboid has 12 face diagonals. Space Diagonals A cuboid has 4 space diagonals. Diagonal Planes A cuboid has 6 diagonal planes. A cuboid net is a two-dimensional pattern that can be folded into a cuboid. The net consists of rectangles arranged in certain forms. The surface area of a cuboid is the total area of all its faces. Formula: Where: SA = surface area p = length l = width t = heigh l = width t = height The volume of a cuboid is the amount of space inside the cuboid. Formula: Where: V = volume p = length l = width t = height Diagonals of a Cuboid Face Diagonal A face diagonal is a line connecting two opposite vertices on the same face. Formulas: and and Space Diagonal A space diagonal is a line connecting two opposite vertices through the inside of the cuboid. Formula:

Net of a cuboid

Definition of a Cylinder A cylinder is a three-dimensional shape that has two parallel circular bases connected by a curved surface. Examples of cylinder-shaped objects include cans, pipes, drums, and water bottles. Elements of a Cylinder Bases A cylinder has 2 circular bases, one at the top and one at the bottom. Curved Surface A cylinder has 1 curved surface connecting the two bases. Radius The radius is the distance from the center of the circle to its edge. Diameter The diameter is twice the radius. Formula: Height The height is the distance between the two circular bases. Net of a Cylinder A cylinder net consists of: two circles one rectangle representing the curved surface Students should understand how the net forms a cylinder when folded. Surface Area of a Cylinder The surface area of a cylinder is the total area of all its surfaces. Formula: Where: SA = surface area r = radius t = height or Students should practice: calculating surface area finding radius or height solving word problems Volume of a Cylinder The volume of a cylinder is the amount of space inside the cylinder. Formula: Where: V = volume r = radius t = height Students should practice: calculating volume finding dimensions from volume solving real-life problems Circumference of the Base Circle The circumference of the circular base can be calculated using: or Where: K = circumference r = radius d = diameter

Net of a Cylinder

Elements of a Cone Base A cone has 1 circular base. Vertex A cone has 1 vertex or apex at the top. Radius The radius is the distance from the center of the base to the edge of the circle. Diameter The diameter is twice the radius. Formula: Height The height is the perpendicular distance from the vertex to the center of the base. Slant Height The slant height is the distance from the vertex to the edge of the circular base. Formula: Where: s = slant height r = radius t = height Net of a Cone A cone net consists of: one circle as the base one sector of a circle as the curved surface Students should understand how these parts form a cone when folded. Surface Area of a Cone The surface area of a cone is the total area of the base and the curved surface. Formula: Where: SA = surface area r = radius s = slant height Students should practice: calculating surface area finding slant height solving word problems Volume of a Cone The volume of a cone is the amount of space inside the cone. Formula: Where: V = volume r = radius t = height Students should practice: calculating volume finding dimensions from volume solving real-life application problems Circumference of the Base Circle The circumference of the base circle can be calculated using: or Where: K = circumference r = radius d = diameter

Net of a Cone

Question 1

A solid shape that has 6 rectangular faces is called …

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Question 2

A cuboid has a length of 10 cm, width of 5 cm, and height of 4 cm. The volume of the cuboid is …

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Question 3

A cylinder has a radius of 7 cm and a height of 10 cm. The volume of the cylinder is …

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Question 4

The number of edges in a cube is …

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Question 5

A cone has a radius of 6 cm and a height of 8 cm. The volume of the cone is …

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Question 6

A solid shape that has a circular base and one vertex is called …

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Question 7

The surface area of a cube with an edge length of 4 cm is …

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Question 8

A cuboid has a length of 12 cm, width of 8 cm, and height of 5 cm. The surface area of the cuboid is …

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Question 9

A cube has an edge length of 9 cm. Find: a. The volume of the cube b. The surface area of the cube

Question 10

A cuboid has a length of 15 cm, width of 10 cm, and height of 8 cm. Find the volume and surface area.

Question 11

A cylinder has a radius of 7 cm and a height of 15 cm. Find the volume of the cylinder.

Question 12

A cone has a radius of 5 cm and a height of 12 cm. Find the volume of the cone.

Question 13

A cuboid has ______ rectangular faces.

Question 14

The distance from the center of a circle to its edge is called the ______.

Question 15

A cylinder and a cone both have ______ bases.

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