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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 43

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 44

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 52

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 45

Observe the following examples, and then do the exercise

Exercise 53

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 46

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 54

: 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 50

Study the following examples

Exercise 55

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 47

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 56

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 51

Study the following examples

Exercise 57

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 48

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 58

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 49

Study the following examples

Example 52

Observe the following examples

Exercise 59

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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