# 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