Surface Areas and Volumes — Question 12

Given,

Diameter of the spherical capsule (d) = 3.5 mm

Radius of the spherical capsule (r) = $\dfrac{\text{Diameter}}{2} = \dfrac{3.5}{2}$ mm = 1.75 mm

Medicine needed to fill the capsule = Volume of the spherical capsule

∴ Medicine needed to fill the capsule (v) = $\dfrac{4}{3}πr^3$

$v = \dfrac{4}{3} \times \dfrac{22}{7} \times (1.75)^3 \\[1em] = \dfrac{4}{3} \times \dfrac{22}{7} \times 5.359375 \\[1em] = \dfrac{88}{21} \times 5.359375 \\[1em] = \dfrac{471.625}{21} \\[1em] = 22.46 \text{ mm}^3$

Hence, the medicine needed to fill the capsule = 22.46 mm³.