A block made of iron is in the shape of a cuboid - OCR - GCSE Maths - Question 9 - 2023 - Paper 5
Question 9
A block made of iron is in the shape of a cuboid.
The block is 3.1 cm by 4.9 cm by 2.2 cm.
The density of iron is 7.87 g / cm³.
Sam thinks that the mass of the block... show full transcript
Worked Solution & Example Answer:A block made of iron is in the shape of a cuboid - OCR - GCSE Maths - Question 9 - 2023 - Paper 5
Step 1
Calculate the Volume of the Block
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To find the volume of a cuboid, use the formula:
V=extlengthimesextwidthimesextheight
Plugging in the dimensions:
V=3.1extcmimes4.9extcmimes2.2extcm=33.49extcm3
For estimation, we can approximate the dimensions as follows:
3 cm, 5 cm, 2 cm
So,
Vext(estimated)=3imes5imes2=30extcm3
Step 2
Calculate the Mass of the Block
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Using the density formula:
extMass=extVolumeimesextDensity
Substituting the values:
extMass=30extcm3imes7.87extg/cm3=236.1extg
We can convert grams to kilograms:
236.1extg=0.2361extkg
Estimating the result as:
240extgext(or0.24kg)
Step 3
Evaluate Sam’s Answer
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Sam thinks the mass is about 2.4 kg. Compared to the estimated mass of about 0.24 kg, Sam's estimate is not reasonable. The estimated mass is significantly lower than what Sam suggested. Therefore, we can conclude that:
Sam’s answer is not reasonable because the estimated mass of 0.24 kg is much less than 2.4 kg.
