A capsule of medicine is in the shape of a sphere of diameter 2.8 mm. How much medicine is needed to fill this capsule (correct to one decimal place)? \(\left(\pi=\frac{22}{7}\right)\)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 11.5 mm3
The medicine needed is the volume of the sphere, \(\frac{4}{3}\pi r^3\), where the radius is half the diameter; the value of \(\pi\) to use is the given \(\frac{22}{7}\).
Radius, half the diameter: \(r=2.8\div2=1.4\) mm
Cube of the radius: \(r^3=1.4\times1.4\times1.4=2.744\)
Volume of the sphere: \(\displaystyle \frac{4}{3}\times\frac{22}{7}\times2.744=\frac{34.496}{3}\approx11.50\,\mathrm{mm^3}\)
Correct to one decimal place, the capsule holds 11.5 mm3 of medicine.