Question

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

• A. Yes
• B. No
• C. Less Data
• D. None of the above

Answer 1

Answer: (B)

No

Radius of cylinder$=1cm$

Height of cylinder$=8cm$

Radius of sphere $=8.5$

Volume of cylinder $=\pi r^{2}h$

$=\pi \times 1^2\times 8$

$=8\pi c{m}^3$

Volume of sphere $=\frac{4}{3}\pi r^3$

$=\frac{4}{3}\pi \times (\frac{8.5}{2}{)}^3$

$=\frac{614125}{6000}\pi c{m}^3$

$\therefore$ total Volume $=(\frac{614125}{6000}+8)\pi$

$=\left(\frac{614125+48000}{6000}\right)\pi$

$=\frac{662125}{6000}\pi$

$=110.35\times 3.41$

$=346.5c{m}^3$

So, $345c{m}^3$ is not correct.