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 i... 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
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Answer
To find the volume of the cuboidal block, we use the formula for the volume of a cuboid:
V=limeswimesh
Where:
l=3.1 cm
w=4.9 cm
h=2.2 cm
Calculating the volume, we find:
V=3.1imes4.9imes2.2=33.1 cm3
Step 2
Calculate the Mass of the Block Using Density
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Answer
We apply the density formula to find the mass:
m=V×ρ
Where:
ρ=7.87 g/cm³ (density of iron)
V=33.1 cm³ (volume calculated previously)
Now, substituting the values:
m=33.1×7.87≈260.07 g=0.260 kg
Step 3
Evaluate Sam's Estimation
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Answer
Sam thinks that the mass of the block is about 2.4 kg. Since our calculated mass is approximately 0.260 kg, this indicates that Sam's estimation is not reasonable. The difference is significant, as Sam's guess is off by around 2.1 kg.
