Question

The volume of the water is a spherical tank is 1470.265 cm3. Determine the depth of water if the tank has a diameter of 30 cm

please help me to answer this in step by step solution​

Answer 1

ans- this is the answer of this question.

Answer 2

Given:

Volume of water in tank = 1470.265 cm³

Diameter of tank = 30 cm

To find:

Depth of water in the tank.

Solution:

Let $d$ be the depth of water in the tank and $D$ be the diameter of the tank. Then, the volume of water, V in the tank is given by the formula:

$V=\frac{1}{3}\pi d^{2} (\frac{3}{2}D-d)$

Substituting the values in the above formula:

$1470.265=\frac{\pi }{3}d^{2} (\frac{3}{2}*30-d)$

$4410.795=\pi d^{2}(45-d)$

$1403.435=d^{2} (45-d)$

where $\pi =3.14$

$1404=45d^{2} -d^{3}$

$d^{3}- 45d^{2} +1404=0$

The roots of the equation are calculated as $d_{1}=44.28,d_{2}=-5.28,d_{3}=6$

Rejecting the first two values and considering $d=6cm$, it is the depth of water in the spherical tank.

Depth of water in a spherical tank having a volume of water 1470.265 cm³ is 6cm.