Question

A spherical glass vessel has a cylindercal neck 8cm long 2cm in diameter the diameter of the spherical part is 8.5cm By measuring the amount of water it holds a child finds its volume to be 345cm cube whether she is correct , taking the above as the insides measurement
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Answer 1

SOLUTION:-

•A spherical glass vessel has a cylindrical neck 8cm long 2cm in diameter of the spherical part is 8.5cm.

To find:

Measurements the volume of 345cm³

She is correct & taking above as the inside measurements.

Explanation:

•Diameter of the spherical part = 8.5cm.

Radius= 8.5/2cm

Now,

Formula of the volume of the sphere;

$= > \frac{4}{3} \pi {r}^{3} \\ \\ = > ( \frac{4}{3} \times 3.14 \times \frac{8.5}{2} \times \frac{8.5}{2} \times \frac{8.5}{2} ) {cm}^{3} \\ \\ = > ( \frac{7713.41}{2} ) {cm}^{3} \\ \\ = > 321.4 {cm}^{3}$

&

Let the radius & h cm be the height of the cylindrical part;

Formula of the volume of the cylinder;

=) πr²h

=) Radius= 2/2 = 1cm

•Height = 8cm

Therefore,

$= > (3.14 \times 1\times 1 \times 8) {cm}^{3} \\ \\ = >25.12 {cm}^{3}$

Quantity of water:

=) (321.4 + 25.12)cm³

=) 346.52cm³

Hence,

Answer is not correct.

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Answer 2

GIVEN:-

$\large\sf\red{height\:(h)\:of\:cylindrical\:part=8cm}$

$\large\sf\red{radius\:(r2)\:of\:cylindrical\:part=1cm}$

$\large\sf\red{radius\:(r1)\:of\:spherical\:part=4.25cm}$

⠀⠀

$\small\sf\blue{Volume\:of\:vessel=Volume\:of\:sphere+Volume\:of\:cylinder}$

$\longrightarrow$$\small\sf\gray{ \frac{4}{3} π {r1}^{3} + π{r2}^{2} h}$

$\longrightarrow$$\small\sf\gray{\frac{4}{3} π {( \frac{8.5}{2}) }^{3} + π {(1)}^{2} (8)}$

$\longrightarrow$$\small\sf\gray{\frac{4}{3} \times 3.14 \times 76.765625 + 8 \times 3.14}$

$\longrightarrow$$\small\sf\gray{321.392+25.12}$

$\longrightarrow$$\small\sf\gray{346.512}$

$\longrightarrow$$\small\sf\gray{{346.51cm}^{3}}$

$\therefore$$\large\tt\underline\pink{Hence,she\:is\:wrong}$