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Advance Geometry Project

“Geometry is the archetype of the beauty of the world.” To understand the spatial skills, starting with nothing is better than geometry. So, let’s initiate to develop these skills by understanding the real-world situations of analyzing shapes and finding figure values.


Spatial and geometric reasoning is not a single ability, skill, or process. By building on strengths and interests that are already present, we can foster an ongoing enthusiasm for mathematics and provide a logical context to develop the number of ideas of the children.


  • Perimeter: It is the distance around the outside of the shape. Perimeter is measured in linear units

  • Area: It is the space inside the flat shape. Area is measured in square units

  • Circumference: It is the distance around the circle. Circumference is measured in linear units

  • Volume: It is the amount of space displaced by a solid 3D shape. Volume is measured in cubic units

  • Surface Area: It is the total area that the surface of 3D shape occupies. Surface area is measured in square units


Rectangle: Area = length x width = lw Perimeter = 2 x length + 2 x width = 2l + 2w

Triangle: Area = ½ x base x height = ½ bh Perimeter = Sum of all sides = a + b + c

Circle: r: Radius: distance from the center to a point on the circle d: diameter: the distance between two points on the circle through the center Circumference = 2𝜋r = 𝜋d (Assume 𝜋 = 3.14)

Dimensional Shapes

Cylinder: Volume = 𝜋r2 x height = 𝜋r2h (Assume 𝜋 = 3.14) Surface = 2𝜋rh + 2𝜋r2 (Assume 𝜋 = 3.14)

Cone: Volume = ⅓ 𝜋r2h (Assume 𝜋 = 3.14) Surface = 𝜋r(r + h2 + r2 ) (Assume 𝜋 = 3.14)

Sphere: Volume = 4/3 𝜋r3 (Assume 𝜋 = 3.14) Surface = 4𝜋r2 (Assume 𝜋 = 3.14)

Word Problems:

  1. Find the volume of a box if its length, breadth, and height are 20 cm, 10.5 cm, and 8 cm respectively.

  2. How much iron is needed to make a rod of length 90 cm and diameter 1.4 cm?

  3. Francisco is making an effort to drink more water and has set a goal of 2 liters per day. He wants to know the volume of the water bottle he takes to school each day. The water bottle is cylindrical and has dimensions of 20 cm height and 4 cm radius.

  4. How much ice cream can be accommodated in a cone with a height of 2 cm and a circular opening radius of 3 cm?

  5. Find the circumference of a playground whose radius is 3 m.


  1. For each of the above problems, write the Given Values

  2. Identify the shape and what is it asking you to calculate

  3. Write the formula for the same

  4. Substitute the values, calculate and write the final answer. Make sure to write the units

Learning Opportunity:

  • Spatial skills play a critical role in the development of mathematics and reading

  • Children learn to make mental images-pictures they can carry in their minds

  • Young children tend to form static images-"still" mental pictures they can refer to

  • Older children are learning to form dynamic images, which they can move or change

  • Problem-solving, analyzing, visualizing incorporates numerous concepts, processes, as well as tools to represent and communicate ideas about space and spatial relationships

Time Required: 30 minutes

Cost: NIL

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