Question

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✒✒A question ⤵⤵⤵

✏✏ À 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 find its volume to beat 345cm³. Check whether she is correct, taking the above as the inside measurements and π = 3.14.✔✔✔

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Answer 1

$\mathfrak\blue{The\:Answer\:Is}$


Volume of Vessel = Volume of Sphere + Volume of Cylinder


$\underline{Volume\:Of\:Sphere}$

Diameter = 8.5 cm

Radius(r)= Diameter / 2

= 8.5 / 2

= 4.25 cm

Volume of Sphere

$= 4 \div 3 \: \times \pi \times r {}^{3}$
$= 4 \div 3 \: \times 3.14 \times (4.25) {}^{3}$
$= 321.39 \: cm {}^{3}$


$\underline{Volume\:Of\:Cylinder}$

Diameter = 2 cm

Radius(r)= Diameter / 2

= 2/2

= 1 cm

Height of cylinder (h) = 8cm

Volume of Cylinder

$= \pi \times r {}^{2} \times h$
$= 3.14 \times (1) {}^{2} \times 8$
$= 25.12 \: cm {}^{3}$


NOW,


Volume of Vessel = Volume of Sphere + Volume of Cylinder

$= 321.39 + 25.12$
$= 346.51 \: cm {}^{3}$


HENCE,
Volume obtained by child is incorrect.

Correct Volume
$= 346.51 \: cm {}^{3}$


$\boxed{Hope\:This\:Helps}$

Answer 2

Solutions :-

Given :
Height of cylinder = 8 cm
Radius of cylinder = 2/2 = 1 cm

Radius of sphere = 8.5/2 = 4.25 cm

Find the volume of cylinder :-

Volume = πr²h cu. unit
= 3.14 × 1² × 8 cm³
= 25.12 cm³

Now,
Find the volume of sphere :-
Volume = 4/3πr³ cu. unit
= 4/3 × 3.14 × (4.25)³ cm³
= 321.39 cm³ (approx)

Find the total volume :-

= Volume of cylinder + volume of sphere
= (25.12 + 321.39) cm³
= 346.51 cm³


Hence,
Volume obtained by child is incorrect.

_______________________

✯ @shivamsinghamrajput ✯