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 it's volume to be 345cm^3. Check whether she is correct. Also find it's actual volume.

Answer 1

Hope this helps no she is not correct.

The actual volume is 346.51 cm3

Answer 2

$\textrm{Volume of vessel = Volume of sphere + Volume of cylinder}$

$\longrightarrow\rm{Volume\: of\: vessel = 4/3\pi r^3+ \pi r^2h=[4/3\times\pi\times r^3]+ [\pi \times r^2\times h]}$

$\longrightarrow\rm{Volume\: of\: vessel=[4/3\times 3.14\times r^3]+ [3.14\times r^2\times h]}$

$\longrightarrow\rm{Volume\: of\: vessel=[4/3\times 3.14\times (Diameter/2)^3]+ [3.14\times (Diameter/2)^2\times h]}$

$\longrightarrow\rm{Volume\: of\: vessel=[4/3\times 3.14\times (8.5/2)^3\:cm^3]+ [3.14\times (2/2)^2\:cm^2\times h]}$

$\longrightarrow\rm{Volume\: of\: vessel=[4/3\times 3.14\times (4.25)^3\:cm^3]+ [3.14\times (1)^2\:cm^2\times h]}$

$\longrightarrow\rm{Volume\: of\: vessel=[4/3\times 3.14\times (4.25)^3\:cm^3]+ [3.14\:cm^2\times h]}$

$\longrightarrow\rm{Volume\: of\: vessel=321.39\:cm^3+ [3.14\:cm^2\times 8\:cm]}$

$\longrightarrow\rm{Volume\: of\: vessel=321.39\:cm^3+25.12\:cm^3=346.51\:cm^3}$

$\boxed{\textrm{Hence we can say that, The child is not correct}}$