Density
5 marks · HardA student wants to determine the density of a cube of wood in the laboratory. She has a ruler, an electronic balance, and a container of water.
Describe how she should measure the mass and the volume of the wood.
Explain why the student should record each measurement three times and calculate an average.
If the mass of the cube is 72.8 g and the length of one edge is 4.0 cm, calculate the density in kg/m³.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) Measure mass using the electronic balance. Measure length of each edge with the ruler, then calculate volume as length³. · must show Use of electronic balance for mass, Use of ruler for edge length, Volume calculated as length × length × length
(b) To reduce random errors and improve accuracy/reliability by taking an average. · must show Improves accuracy/reduces errors, Averages out random measurement variations
(c) 1.1 × 10³ kg/m³
Common mistakes: Forgetting to convert cm to m; Not cubing length for the volume
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · States correct instruments: balance for mass, ruler for length.
M2 (a) · 1 mark · States volume = length³ or measures all three edges.
B1 (b) · 1 mark · Mentions improving accuracy/reliability or reducing errors by averaging.
B2 (b) · 1 mark · Explains it reduces effect of random errors or measurement inconsistencies.
A1 (c) · 1 mark · Final answer 1.1 × 10³ kg/m³ (accept 1100 kg/m³) with correct method and unit.
Worked solution
a) Measure mass using the electronic balance. Measure length of each side using a ruler. As the cube has equal sides, volume = (length)³.
b) Repeating measurements and averaging helps reduce the effect of random errors, making your result more accurate and reliable.
c) Volume = 4.0 cm × 4.0 cm × 4.0 cm = 64 cm³ = 0.000064 m³
Mass = 72.8 g = 0.0728 kg
Final answer to 2 s.f.: 1.1 × 10³ kg/m³