Question

A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter o the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345 cm³. Check whether she is correct, taking the above as the inside measurements, and \(\pi = 3.14.\)

Answer 1

The height (h) of the cylindrical part is 8 cm.
The radius (r₂) of the cylindrical part is 1 cm.
The radius (r₁) of the spherical part is 4.25 cm.
The volume of the vessel is the sum of the volume of the sphere and the volume of the cylinder:
\(=\frac{4}{3}\pi r^3_1+\pi r_2^2h\)

\(=\frac{4}{3}\pi(8.52)^3+\pi(1)^2(8)\)

\(=\frac{4}{3}×3.14×76.765625+8×3.14\)
\(=321.392+25.12\)
\(=346.51\ \text{cm}^3\)
Therefore, her conclusion is incorrect.