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

What is the surface area of the rectangular prism below?

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 triangular prism has a length of 8 cm, width of 5 cm and height of 6 cm. What is its volume?

A composite shape is formed by combining a rectangular prism and a cylinder. What is the total surface area of the composite shape?

A sphere has a diameter of 14 cm. What is its volume?

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.

Test your understanding of surface area, volume, and capacity of 3D shapes and composite shapes with the help of diagrams. Suitable for Year 10 maths students.