Year 10 Maths: Surface Area, Volume, Capacity of 3D Shapes

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Questions and Answers

What is the surface area of the rectangular prism below?
PLP2UjK.png

  • 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?
k1Kf9Qo.png

  • 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?
ypRJG9d.png

  • 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?
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<p>1250 cm$^2$ (D)</p>
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A sphere has a diameter of 14 cm. What is its volume?
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<p>1571.5Ï€ cm$^3$ (C)</p>
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Flashcards

Surface Area of a Rectangular Prism

The total area of all the faces of the rectangular prism, calculated to be 472 cm² in the example.

Volume of a Cylinder

The amount of space inside the cylinder, calculated as 640π cm³.

Volume of a Triangular Prism

The amount of space inside the triangular prism, calculated as 160 cm³.

Surface Area of a Composite Shape

The total area covering the outside of the combined rectangular prism and cylinder shape, calculated to be 1250 cm².

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Volume of a Sphere

The amount of space inside the sphere, calculated to be 1571.5π cm³.

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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: Ï€r²h, 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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