Question

PLEASE HELP!

Answer 1

Answer:

The height of the water is $60.5\ ft$

Step-by-step explanation:

step 1

Find the volume of the tank

The volume of the inverted right circular cone is equal to

$V=\frac{1}{3}\pi r^{2} h$

we have

$r=16\ ft$

$h=96\ ft$

substitute

$V=\frac{1}{3}\pi (16)^{2} (96)$

$V=8,192\pi\ ft^{3}$

step 2

Find the 25% of the tank’s capacity

$V=(0.25)*8,192\pi=2,048\pi\ ft^{3}$

step 3

Find the height, of the water in the tank  

Let

h ----> the height of the water  

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

$\frac{R}{H}=\frac{r}{h}$

substitute

$\frac{16}{96}=\frac{r}{h}\\ \\r= \frac{h}{6}$

where

r is the radius of the smaller cone of the figure

h is the height of the smaller cone of the figure

R is the radius of the circular base of tank

H is the height of the tank

we  have

$V=2,048\pi\ ft^{3}$ -----> volume of the smaller cone

substitute

$2,048\pi=\frac{1}{3}\pi (\frac{h}{6})^{2}h$

Simplify

$221,184=h^{3}$

$h=60.5\ ft$