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 \( \pi \ = \ 3.14 \)

Volume of spherical vessel = Volume of sphere + Volume of cylinder

\(= \ \pi (1)^2 (8) \ + \ \frac{4}{3} \pi (4.25)^3 \)

\(= \ 3.14(8 \ + \ \frac{4}{3} \ × \ 76.765625) \ \)

\( = \ 3.14(8 \ + \ 102.353 ) \)

\( = \ 3.14 \ × \ 110.353 \ \)

\( = \ 346.51 \) cm³

\(\therefore \) She is incorrect. The correct answer is 346.51 cm³