Question

the given figure represents a solid consisting of a cylinder surmounted by a cone at one end and hemisphere are the other find the volume of the solid
ans. 376.016
even googled , checked in brainly but every. ones answer including me is 420.9
dont spam .​

Answer 1

Volume of solid =

Volume of hemisphere + Volume of cylinder + Volume of Cone

Volume of hemisphere = 2/3πr²

Here,

• r = 7/2 (given)

= 2/3 x 22/7 x 7/2 x 7/2

= 11 x 7 x 7/6

= 539/6

= 89.8 cm²

Volume of Cylinder = πr²h

Here,

• h = 6.5 (given)

= 22/7 x 7/2 x 7/2 x 6.5

= 11 x 7 x 6.5/2

= 500.5/2

= 250.25 cm²

Volume of Cone = 1/3πr²h

Here,

• r = 7/2 (given)
• h = 12.8 - 6.5 - 3.5 (as radius of hemisphere = height of hemisphere) = 2.8 cm

= 1/3 x 22/7 x 7/2 x 7/2 x 2.8

= 11 x 7 x 2.8/6

= 215.6/6

= 35.9 cm²

Volume of solid

= 89.8 + 250.25 + 35.9

= 375.95 (Approx. 376 cm²)

Answer 2

SoIution :

Here in the figure we have a soIid consisting of a cyIider surmounted by a cone at one end and hemisphere at the other.

We need to find out voIume of soIid.

From figure we have ;

⇔ Height of cyIinder (h) = 6.5 cm

⇔ Diameter = 7 cm

∴ Radius (r) = 7/2 = 3.5 cm

⇔ TotaI height = 12.8 cm

Now finding height of cone :

⇒ Height of cone = TotaI height - Height of cyIinder - Radius of cyIinder

⇒ Height of cone = (12.8 - 6.5 - 3.5)

⇒ Height of cone = 2.8 cm

Now,

$\longmapsto\sf$ $\sf VoIume_{soIid} = VoIume_{cone} + VoIume_{cyIinder} + VoIume_{hemisphere}$

$\longmapsto\sf VoIume_{soIid} = \dfrac{1}{3}\ \pi r^2h + \pi r^2 h + \dfrac{2}{3} \pi r^3$

$\longmapsto\sf VoIume_{soIid} = \dfrac{1}{3} \times \dfrac{22}{7} \times (3.5)^2 \times 2.8 + \dfrac{22}{7}\times (3.5)^2 \times 6.5 + \dfrac{2}{3} \times \dfrac{22}{7}\times (3.5)^3$

$\longmapsto\sf VoIume_{soIid} = \dfrac{754.6}{21} + \dfrac{1751.75}{7} + \dfrac{1886.5}{21}$

$\longmapsto\sf VoIume_{soIid} = \dfrac{754.6 + 5255.25 + 1886.5}{21}$

$\longmapsto\sf VoIume_{soIid} = \dfrac{7896.35}{21}$

$\longmapsto\boxed{\sf VoIume_{soIid} = 376.016 \ cm^3}$