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 350 cm^3. Check whether she is correct, taking the above as the inside measurements, and π = 3.14.

Answer 1

Answer:

Correct option is

B

No

Radius of cylinder=1cm

Height of cylinder=8cm

Radius of sphere =8.5

Volume of cylinder =πr

2

h

=π×1

2

×8

=8πcm

3

Volume of sphere =

3

4

πr

3

=

3

4

π×(

2

8.5

)

3

=

6000

614125

πcm

3

∴ total Volume =(

6000

614125

+8)π

=(

6000

614125+48000

)π

=

6000

662125

π

=110.35×3.41

=346.5cm

3

So, 345cm

3

is not correct.

Answer 2

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

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

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

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

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

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

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

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

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

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