Question

A spherical glass vessel has a cylindrical neck 8 cm long ,2cm in diameter the diameter of spherical part is 8.5cm find its volume

Answer 1

$\huge{\bf{\underline{\pink{Answer :}}}}$

Given,

→Height of Spherical glass - 8 cm

→First Radius [$\bold{r_{1}}$] of Spherical part - $\bold{\frac{8.5}{2} = \bold{4.25\ cm}}$

→Second Radius[$\bold{r_{2}}$] of Cylindrical part - $\bold{\frac{2}{2}} = \bold{1 \ cm }}$

We know that :

Volume of glass vessel = Volume of sphere + Volume of Cylindrical

∴ $\implies \bold{\frac{4}{3} \pi[ r_{1}]^{3}} +\bold{ \pi[ r_{2}]^{2}}h$

$\implies \bold{\frac{4}{3} \pi [4.25]^{3}} + \bold{ \pi [ 1] ^{2} [8]}$

$\implies \bold{\frac{4}{3} \ x \ 3.14 \ x \ 76.765625 \ + \ 8 \ x \ 3.14}$

$\implies \bold{321.392 \ + \ 25.12}$

$\implies \bold{346.512 \ cm }$ .......Answer

Answer 2

Answer:

${\sf {\boxed {\boxed{346.51 {m}^{3} }}}}$

Step-by-step explanation:

Given :

Length of cylindrical neck = 8cm

Diameter of cylindrical neck = 2cm

Diameter of Spherical part = 8.5cm

To find :

Volume = ?

Solution:

$\sf \red{volume \: of \: vessels = volume \: of \: sphere \: + volume \: of \: cylinder}$

$\rm\blue {\underline{volume \: of \: sphere}} \\ \orange {\rm{diameter = 8.5cm}} \\ \rm \orange{radius = \frac{diameter}{2} = \frac{8.5}{2} = 4.25 \: cm} \\ \orange{ \rm { \: volume \: of \: sphere \: = \frac{4}{3} \pi {r}^{3}}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm \orange{ = \frac{4}{3} \times 3.14 \times ( {4.25 }^{3} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm \orange{ = 321.39 {cm}^{3} }$

$\\ {\underline {\rm{\blue {volume \: of \: cylinder}}}} \: \\ \\ \\ \rm \green{diameter = 2cm} \\ \rm \green{radius = \frac{diameter}{2} = \frac{2}{2} = 1cm} \\ \rm \green{height \: of \: cylinder \: = 8cm} \\ \rm \green{volume \: of \: cylinder = \boxed{\pi {r}^{2}h}} \\ \rm \green{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3.14 \times ( {1}^{2}) \times (8)} \\ \rm \green{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 12.12cm}$

$\rm \pink{volume \: of \: vessel = volume \: of \: sphere + volume \: of \: cylinder} \\ \rm \pink{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 321.39 + 25.12} \\ {\rm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \pink {\boxed {\boxed{ = 346.51c {m}^{3}}}}}$