Percentage growth of a ball whose mass varies as the cube of its radius
Percentage growth of a ball whose mass varies as the cube of its radius
IP 2
8 marks
The mass \(m\) grams of a solid metal ball is directly proportional to the cube of its radius \(r\) cm. A ball of radius \(3\) cm has a mass of \(216\) g.
- Find the mass of a ball of radius \(5\) cm.[2]
- A second ball has a mass that is \(72.8\%\) greater than the mass of a third ball. Find the percentage by which the radius of the second ball is greater than the radius of the third ball.[3]
- Show that, for any \(p>0\), increasing the radius by \(p\%\) increases the mass by more than \(3p\%\).[3]
Solution:
Solution locked
680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs tuition enrolment.
Create a free account to practise similar questions.
Answer:(a) \(1000\text{ g}\) (b) \(20\%\) (c) Shown: increase \(=3x+3x^2+x^3>3x\) where \(x=\dfrac{p}{100}\)
Need help? Join our IP Math tuition programme.
Learn more