Question

Question 8
A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345 $c{m}^3$. Check whether she is correct, taking the above as the inside measurements, and $\pi =3.14$.

Answer 1

Radius of cylinder = 1 cm, height of cylinder = 8 cm, radius of sphere = 8.5 cm
Volume of cylinder
$=\pi r^{2}h$
$=\pi \times 1^2\times 8$
$=8\pi c{m}^3$
Volume of sphere
$=\frac{4}{3}\pi r^3$
$=\frac{4}{3}\pi \times {\left(\frac{8.5}{2}\right)}^3$
$=\frac{614125}{6000}\pi c{m}^3$
Total volume = Volume of sphere + Volume of cylinder
$=(\frac{614125}{6000}+8)\pi$
$=\left(\frac{614125+48000}{6000}\right)\pi$
$=346.51c{m}^3$