MATH SOLVE

4 months ago

Q:
# A water tank in the shape of an inverted cone has a height of 11 feet and a radius of 6.0 feet. Find the volume of the water tank when the water is 7 feet deep.

Accepted Solution

A:

Answer:
A water tank in the shape of an inverted cone has a height of 11 feet and a radius of 6.0 feet. The volume of water in a conical tank is 107 cubic feet.
Solution:
Consider the figure attached below as side view of inverted cone shape. AG = BG = 6 feet [Radius ]
OG = 11 feet [water tanks height ]
OE = 7 feet [Depth of water ]
Need to calculate EC first , which is radius of uppermost surface till where the water is filled.
Consider triangle OEC and triangle OGB
Angle OEG = Angle OGB [both are 90^{\circ}]
Angle GOB = Angle EOC [Same angle]
So using Angle angle similarity criterion, it can be said that
Triangle OEC is similar to triangle OGB. [tex]\frac{\mathrm{OE}}{\mathrm{O} \mathrm{G}}=\frac{\mathrm{EC}}{\mathrm{GB}}[/tex] [Ratio of corresponding side of similar triangles ]
[tex]\frac{7}{11}=\frac{E C}{6}[/tex][tex]\mathrm{EC}=\frac{42}{11} \text { feet }[/tex]
Volume of water = Volume of cone of height 7 feet and radius 42/11 feet
Formula for volume of cone = [tex]\pi r^{2} h=\pi \times\left(\frac{42}{11}\right)^{2} \times \frac{7}{3}[/tex]
= 106.909 which is approximately 107Hence volume of water in a conical tank is 107 cubic feet.