Test your knowledge: Surface area of composite solids exam questions.

📚 Quick Study Guide

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• Basic Surface Area Formulas: Remember these key formulas:
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• Sphere: $4\pi r^2$
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• Cylinder: $2\pi r h + 2\pi r^2$ (including top and bottom)
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• Cube: $6s^2$ (where $s$ is the side length)
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• Rectangular Prism: $2(lw + lh + wh)$
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• Composite Solids: These are made up of two or more basic solids. To find the surface area:
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• Calculate the surface area of each individual solid.
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• Identify any overlapping areas where the solids join.
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• Subtract the overlapping areas from the total surface area. For example, if a cylinder sits on a cube, subtract the area of the circle on the cylinder's base and the corresponding area on the cube's top face.
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• Hidden Surfaces: Watch out for surfaces that might be hidden when the solids are combined. Do not include these hidden surfaces in the total surface area.
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• Units: Ensure all measurements are in the same units before calculating. The surface area will be in units squared (e.g., $cm^2$, $m^2$).

🧪 Practice Quiz

1. A composite solid is formed by placing a cube with side length 5 cm on top of another cube with side length 3 cm. What is the surface area of the composite solid, excluding the overlapping area?

   1. 150 $cm^2$
   2. 154 $cm^2$
   3. 176 $cm^2$
   4. 184 $cm^2$

2. A hemisphere of radius 4 cm is attached to a cylinder of radius 4 cm and height 10 cm. What is the total surface area of the composite solid (including the base)?

   1. $439.82$ $cm^2$
   2. $502.65$ $cm^2$
   3. $552.92$ $cm^2$
   4. $603.19$ $cm^2$

3. A cone with a radius of 3 cm and a slant height of 5 cm sits on top of a cube with sides of 6 cm. Calculate the total surface area of the composite solid.

   1. $246.37$ $cm^2$
   2. $252.46$ $cm^2$
   3. $262.37$ $cm^2$
   4. $276.37$ $cm^2$

4. Two identical rectangular prisms with dimensions 2 cm x 3 cm x 4 cm are joined face to face, such that the 3 cm x 4 cm faces are touching. Find the surface area of the resulting solid.

   1. $52$ $cm^2$
   2. $50$ $cm^2$
   3. $40$ $cm^2$
   4. $48$ $cm^2$

5. A solid is made by drilling a cylindrical hole of radius 1 cm through a cube of side 4 cm. If the hole is drilled from one face to the opposite face, what is the surface area of the resulting solid?

   1. $126.83$ $cm^2$
   2. $120.56$ $cm^2$
   3. $122.28$ $cm^2$
   4. $124.72$ $cm^2$

6. A sphere of radius 2 cm is placed inside a cube with sides of 6 cm. What is the surface area of the cube that is *not* covered by the sphere?

   1. $190.86$ $cm^2$
   2. $175.75$ $cm^2$
   3. $180.97$ $cm^2$
   4. $185.44$ $cm^2$

7. A composite solid is created by attaching a triangular prism to a rectangular prism. The triangular prism has a base of 4 cm, a height of 3 cm, and a length of 8 cm. The rectangular prism has dimensions 4 cm x 5 cm x 8 cm. If the triangular prism sits on the 4 cm x 8 cm face of the rectangular prism, what is the surface area of the composite solid?

   1. $268$ $cm^2$
   2. $284$ $cm^2$
   3. $300$ $cm^2$
   4. $316$ $cm^2$