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Questions and Answers
What is the surface area of the rectangular prism below?
What is the surface area of the rectangular prism below?
- 440 cm$^2$
- 472 cm$^2$ (correct)
- 410 cm$^2$
- 504 cm$^2$
A cylindrical tank with a radius of 4 cm and height 10 cm is filled with water. What is the volume of water in the tank?
A cylindrical tank with a radius of 4 cm and height 10 cm is filled with water. What is the volume of water in the tank?
- 500Ï€ cm$^3$
- 800Ï€ cm$^3$
- 640Ï€ cm$^3$ (correct)
- 400Ï€ cm$^3$
A triangular prism has a length of 8 cm, width of 5 cm and height of 6 cm. What is its volume?
A triangular prism has a length of 8 cm, width of 5 cm and height of 6 cm. What is its volume?
- 140 cm$^3$
- 180 cm$^3$
- 120 cm$^3$
- 160 cm$^3$ (correct)
A composite shape is formed by combining a rectangular prism and a cylinder. What is the total surface area of the composite shape?
A composite shape is formed by combining a rectangular prism and a cylinder. What is the total surface area of the composite shape?
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A sphere has a diameter of 14 cm. What is its volume?
A sphere has a diameter of 14 cm. What is its volume?
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Study Notes
Surface Area of 3D Shapes
- The surface area of a 3D shape is the total area of all its surfaces.
Volume of 3D Shapes
- The volume of a 3D shape is the amount of space inside the shape.
- Measured in cubic units (e.g. cubic centimeters, cubic meters).
Capacity of 3D Shapes
- The capacity of a 3D shape is the amount of liquid or substance it can hold.
- Measured in units of volume (e.g. liters, milliliters).
3D Composite Shapes
- Made up of multiple simple 3D shapes combined together.
- Examples: rectangular prism with a cylinder on top, or a triangular prism attached to a rectangular prism.
Important Formulas
- Surface area of a rectangular prism: 2(lw + lh + wh), where l, w, and h are the length, width, and height.
- Volume of a rectangular prism: lwh.
- Volume of a cylinder: πr²h, where r is the radius and h is the height.
Key Concepts
- Be able to calculate the surface area and volume of various 3D shapes.
- Understand how to break down composite shapes into simpler shapes.
- Recognize and apply the correct formulas for different shapes.
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