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Grade 10 Mathematics Learners’ Book

INNODEMS

Section 2.7 Surface Area and Volume of Solids

Surface Area.

Activity 2.7.1.

\(\textbf{Materials Needed:}\)
  1. Solids made of cardboard or plastic (cube, rectangular prism, cylinder, cone, pyramid, sphere)
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  2. Grid paper or plain paper
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  3. Scissors, rulers, tape, glue and String (for measuring curved edges like the circumference of a circle)
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  4. Pre-made nets of solids (optional)
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  • Worksheet to record observations and answers
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  • Choose one solid object (e.g., cube, cone, cylinder).
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  • Create a net for their object (either by unfolding a model or using printed templates).
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  • Trace the faces onto grid paper or measure them using a ruler or string.
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  • Calculate the area of each face using appropriate formulas.
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  • Add up all face areas to find the total surface area.
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  • For cylinders and cones, use a string to measure the curved part.
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\(\textbf{Extended Activity}\)
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Wrap or cover real items (e.g., a cereal box, soda can) using calculated surface area. Design a custom box or can with a specific surface area for packaging a product.
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\(\textbf{Study Questions}\)
  1. How did your net help you find the surface area?
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  2. What would happen if your object was twice as big — would surface area double?
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  3. Derive and apply surface area formulas using practical reasoning and measurement.
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\(\textbf{Key Takeaway}\)
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Surface area is the total area of the exposed or outer surfaces of a prism.
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🔹A right prism is a geometric solid that has a polygon as its base and vertical faces perpendicular to the base. The base and top surface are the same shape and size. It is called a “right” prism because the angles between the base and faces are right angles.
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🔹 The name given to the solid that is unfolded this way is called a net. When a prism is unfolded into a net, we can clearly see each of its faces.
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🔹 We can thereby clearly calculate the surface area by finding the area of each faces and add them all together to get the surface area of the Prism.
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🔹 For example, If we are given a cylinder, the top and bottom faces are circles and the curved area is like a rectangle. So when finding it’s surface area we find the area of the two circles and the area of the rectangle then we add all these areas all together to compute the cylinder’s surface area.
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