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Grade 10 Mathematics Learners’ Book

INNODEMS

Subsection 2.7.1 Surface area of Prisms

Activity 2.7.2.

A cube is unfolded to a net made up of 6 identical squares .
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\(\textbf{Materials needed.}\)
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  • Paper Folds of multiple cubes.
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  • Rulers
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  • Glue
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    🔹 Measure the side length (s) of one smaller square on a face.
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    🔹 Count how many squares make up one face for example, a 3x3 or 4x4
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    🔹 Make an entire cuboid.
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    🔹 Count how many squares make up the cuboid.
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  • Discuss in your groups what will happen if the surface area doubles in size.
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    🔹 Why do bigger cubes have more surface area?
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\(\textbf{Key Takeaway}\)
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🔹 A prism is a Geometric object with two identical, parallel bases and straight sides connecting them.
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🔹Examples of right prisms are cylinders, rectangular prisms, cubes and triangular prisms.
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\(\textbf{Types of Prisms}\text{:}\) Rectangular and cube prisms, Triangular Prisms and Cylinders.
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\(\textbf{Surface Area of a cube}\)
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Observe the cuboid below whose side is 8cm.
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Example 2.7.1.

(a). Work out the surface area of the cube whose side is 8cm.
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Solution.
(b).The surface area of the cube.
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The area of one face.
\begin{align*} = \amp 8 \,\text{cm} \times 8 \, \text{cm} \\ = \amp 64 \, \text{cm}^2 \end{align*}
There are 6 faces therefore the surface area of the cube is;
\begin{align*} = \amp 6 \, \times 64 \, \text{cm}^2\\ = \amp 384 \, \text{cm}^2 \end{align*}
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The surface area of the cube is 384 \(\text{cm}^2\)
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\(\textbf{Exercise}\)
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1.A large wooden dice with sides measuring 12 cm each is to be painted on all six faces. If one milliliter of paint covers 5 cm², calculate the total amount of paint required to cover the dice completely.
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2. A cube has a side length of 25 cm. If the cost of the cardboard material is Ksh.110 per square centimeter, determine the total cost of making one box. How much would it cost to produce 500 such boxes?
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3. A decorative gift box is shaped like a cube with each side measuring 18 cm. To wrap it completely, calculate the total area of wrapping paper needed. If the shop sells wrapping paper in sheets of 1 square meter, how many sheets will be required to wrap 20 such gift boxes?
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4. A small storage room is designed in the shape of a cube with an edge length of 4 meters. The floor, four walls, and ceiling all need to be tiled. If each tile covers an area of 0.5 square meters, determine the total number of tiles required to fully cover the interior of the room
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5. A cube-shaped metal water tank with a side length of 2.5 meters is being coated with a protective layer on all its surfaces to prevent rusting. If the coating material costs Ksh.150 per square meter, calculate the total cost to coat the entire tank.
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6. A pet shop wants to construct a cube-shaped aquarium with a side length of 1.2 meters. The aquarium needs to be made entirely of glass, including the base and all four vertical sides, \(\textbf{but the top will remain open}.\) If the cost of glass is Ksh. 750 per square meter, find the total cost of constructing the aquarium.
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7. A company is designing a cube-shaped promotional stand with a side length of 5 meters. The stand will be covered with high-quality wallpaper on all six faces. If one roll of wallpaper covers 10 square meters, determine the number of rolls required to fully cover the cube.
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