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 cm³. Check whether she is correct, taking the above as the inside measurements, and π=3.14.

Given:
Height (h) of cylindrical part = 8 cm
Radius (r2) of cylindrical part = 2/2 = 1 cm
Radius (r1) of spherical part = 8.5/2 = 4.25 cm
Volume of vessel = Volume of sphere + Volume of cylinder
= (4/3)πr1³ + πr2²h
= (4/3)π(4.25)³ + π(1)²(8)
= (4/3) × 3.14 × 76.765625 + 8 × 3.14
= 321.392 + 25.12
= 346.51 cm³
So, the child's measurement is wrong.