Volume Notes

Surface Area Quiz Review

  • Sphere: Surface area formula is 4πr24 \pi r^2. Remember to halve the diameter to get the radius.
  • Cone: Surface area formula is πr2+πrl\pi r^2 + \pi r l, where ll is the slant height. Ensure correct units and round appropriately.

Volume

  • Volume is the amount of space inside a solid (3D).
  • Measured in cubic units (e.g., cubic millimeters, cubic centimeters, cubic meters, cubic kilometers).

Conversion Between Units

  • 1 cm3=1000 mm31 \text{ cm}^3 = 1000 \text{ mm}^3
  • 1 m3=1,000,000 mm31 \text{ m}^3 = 1,000,000 \text{ mm}^3
  • 1 km3=1,000,000,000 mm31 \text{ km}^3 = 1,000,000,000 \text{ mm}^3
  • When converting from smaller to larger units, divide.
  • When converting from larger to smaller units, multiply.

Volume Formulas

  • Cube: V=s3V = s^3 (where ss is the side length).
  • Rectangular Prism: V=l×b×hV = l \times b \times h (length x breadth x height).
  • Prism: V=AhV = Ah (where AA is the area of the cross-section and hh is the height/distance between the two cross-sections).
  • Cylinder: V=πr2hV = \pi r^2 h

Capacity

  • Capacity is the amount of liquid that fits in a solid, measured in milliliters, liters, kiloliters, etc.
  • 1L=1000mL1 \text{L} = 1000 \text{mL}
  • 1kL=1000L1 \text{kL} = 1000 \text{L}
  • 1cm3=1mL1 \text{cm}^3 = 1 \text{mL}
  • 1m3=1kL1 \text{m}^3 = 1 \text{kL}
  • To find the capacity, calculate the volume first and then convert the units:
    • Cubic meters convert to kiloliters.
    • Cubic centimeters convert to milliliters.