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Volume of a cube

A cube is a three-dimensional shape with 6 equal square faces, 12 edges, and 8 vertices (corners). All sides are equal in length.

Identify concept of a cube

Learn about a cube in a fun way.

Activity 1

Study the following information: A cube is a three-dimensional (3D) solid shape in which:

All faces are squares
All edges are equal in length
All angles are right angles (90°)
Faces: A cube has 6 square faces.
Edges: A cube has 12 edges, all the same length.
Vertices (Corners): A cube has 8 vertices.
Dimensions: A cube has length = width = height. (All sides are equal.)

The below figure represent a cube

Construct net of a cube

How to construct a net of a cube.

Activity 2

A net of a cube is a flat (2D) arrangement of six equal squares that can be folded to form a cubeFollow the instructions below and construct the net of a cube

The below diagrams show the net of a cube

net of a cube

Exercise 1

By using the net of cube, design the following cubes

Cube of side 10 cm
Cube of side 15 cm
Cube of side 20 cm
Cube of side 8 cm

Calculate volume of a cube

Activity 3

Observe the following examples, and then do the exercise

Exercise 2

Calculate the following

1. Find the volume of a cube with side 3 cm.
2. Find the volume of a cube with side 5 cm.
3. A cube has side 8 m. Find its volume.
4. A small cube-shaped box has a side length of 4 cm.How much space is available inside the box?
5. A cube-shaped water tank has sides measuring 2 m. What is the maximum volume of water the tank can hold?
6. A cube-shaped gift package has an edge length of 10 cm. Calculate the volume of the package.
7. An ice cube has sides of 3 cm. How much ice (volume) is contained in the cube?
8. A carpenter makes a cube-shaped wooden block with side 6 cm. Find the volume of the block.
9. A cube has volume 64 cm³. Find the side length.
10. A cube has volume 125 m³. Find the side length.

Volume of rectangular prism

A rectangular prism is a three-dimensional shape with 6 rectangular faces, 12 edges, and 8 vertices. Its opposite faces are equal, and its length, width, and height can be different.

Identify concept of rectangular prism

Activity 4

Study the following informationA rectangular prism (also called a cuboid) is a three-dimensional (3D) solid shape where:

All faces are rectangles
Opposite faces are equal and parallel
All angles are right angles (90°)
Faces: It has 6 rectangular faces.
Edges: It has 12 edges.
Vertices (Corners): It has 8 vertices.
Dimensions: It has length (l), width (w), and height (h). (These may be different.)

Construct net of rectangular prism

A net of a rectangular prism is a flat (2D) arrangement of six rectangles that can be folded to form a 3D box shape.Construct with Paper

Draw one rectangle (this will be the front face). ·
Attach another rectangle of the same size to the right (the side face). ·
Attach another rectangle to the left (the other side). ·
Attach one rectangle above (the top face). ·
Attach one rectangle below (the bottom face). ·
Finally, attach one rectangle behind the front (the back face).

net of rectangular prism

Net of a rectangular prism

Exercise 3

: By using net of rectangular prism, design the rectangular prism with sides

8cm by 6cm by 9 cm
10 cm by 13 cm by 17 cm
10cm by 15 cm by 16cm

Calculate volume of a rectangular prism

Example 1

Study the following examples

Exercise 4

Calculate the volume of the following

1. A water tank has length of 3 m, width of 2 m, and height of 1.5 m. Find its volume.
2. A box measures 40 cm × 25 cm × 20 cm. Calculate the space inside the box.
3. A cupboard is 2 m long, 0.5 m wide, and 1.8 m high. Find its volume.
4. A brick has dimensions 20 cm × 10 cm × 8 cm. Find its volume.
5. A fish tank measures 60 cm × 30 cm × 35 cm. How much water can it hold?
6. A package measures 25 cm × 18 cm × 12 cm. Find its volume.
7. A beam has dimensions 4 m × 0.3 m × 0.2 m. Calculate its volume.
8. A refrigerator interior measures 80 cm × 50 cm × 40 cm. Find the storage capacity.
9. A juice carton measures 10 cm × 6 cm × 20 cm. Find its volume.
10. A container measures 2.5 m × 1.2 m × 0.8 m. Calculate the volume of sand it can hold.

Volume of triangular prism

A prism is a three-dimensional (3D) shape that has: Two identical and parallel faces called bases Flat rectangular or parallelogram faces connecting the bases The same cross-section throughout its length

Identify the concept of triangular prism

Activity 5

Study the Following Information A triangular prism is a three-dimensional (3D) solid shape where:

The bases are triangles
The side faces are rectangles
The triangular faces are equal and parallel
Faces: It has 5 faces → 2 triangular faces + 3 rectangular faces
Edges: It has 9 edges
Vertices (Corners): It has 6 vertices

The images below show how triangular prism is look like

Triangular prism

Construct a net of triangular prisms

A net of a triangular prism is a flat (2D) arrangement that folds into the prism.Construct with Paper

Draw a triangle (this will be the base)
Draw three rectangles attached to each side of the triangle
Draw another triangle attached to one rectangle (second base)

Net of a triangular prism

Exercise 5

Design triangular prisms with:

Triangle base = 6 cm, height = 4 cm, length = 10 cm
Triangle base = 8 cm, height = 5 cm, length = 12 cm
Triangle base = 10 cm, height = 6 cm, length = 15 cm

Calculate volume of triangular prism

Example 2

Study the following examples

Exercise 6

Find the volume of:

A roof of a small house is shaped like a triangular prism. The base of the triangle is 6 m, height 4 m, and the length of the roof is 10 m. How much space does the roof enclose?
A tent has a triangular base with a base 5 m and a height 3 m, and a length of 8 m. Find the volume of the tent.
A triangular prism-shaped aquarium has a triangle base of 7 cm, height 5 cm, and length 12 cm. How much water can it hold?
A wooden wedge has a triangular base with base of 8 cm, a height 6 cm, and length 15 cm. Calculate the volume of the wedge.
A triangular prism-shaped chocolate mold has a triangle base of 4 cm, height 3 cm, and length 10 cm. What is the volume of chocolate it can hold?

Volume of cylinder

Identify concept of cylinder

what is a cylinder

Cylinder

Real word shapes of cylinders

Activity 6

Study the Following InformationA cylinder is a three-dimensional (3D) solid shape where:

The bases are circle.
The sides are curved
The bases are equal and parall
Faces: It has 2 circular faces
Edge: It has 1 curved surface
Vertices: It has no vertices
Dimensions: It has radius (r) and height (h)

Construct net of cylinder

Observe the following figureA net of a cylinder consists of:

One rectangle (curved surface)
Two circles (top & bottom)

Exercise 7

Draw nets for cylinders

Radius = 3 cm, Height = 8 cm
Radius = 5 cm, Height = 10 cm
Radius = 4 cm, Height = 12 cm

Calculate volume of cylinder

Activity 7

Study the following examples

Example 3

Observe the following examples

Exercise 8

Find the volume of the following:

A water tank is cylindrical with radius 3 m and height 5 m. Find the maximum volume of water it can hold.
A juice can has a radius of 5 cm and height of 12 cm. How much juice does it contain?
A cylindrical drum has radius 2 m and height 4 m. Calculate the volume of the drum.
A pillar is shaped like a cylinder with radius 1.5 m and height 6 m. What is the volume of the pillar?
A cake is baked in a cylindrical pan with radius 10 cm and height 5 cm. Find the volume of the cake.
A cylindrical tank in a farm has radius 4 m and height 3 m. Find the amount of water it can store.
A soda can has a radius 3 cm and height 12 cm. Calculate its volume.
A cylindrical candle has a radius of 7 cm and height of 20 cm. How much wax is needed to fill it?
A water bottle is shaped like a cylinder with radius 5 cm and height 25 cm. Find its volume.
A silo in a farm has a radius 6 m and height 15 m. Determine the volume of grains it can hold.

Mathematics

VOLUME

Mathematics Standard VII Topics

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