Water is stored in a cylindrical tank with a diameter of 36 feet. The surface area of the tank is 4750.1 square feet. What is the height of the tank?

defazajx 2021-01-02 Answered
Water is stored in a cylindrical tank with a diameter of 36 feet. The surface area of the tank is 4750.1 square feet. What is the height of the tank?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Layton
Answered 2021-01-03 Author has 16602 answers

The surface area of a cylinder is given by the formula \(S= 2\pi r^{2}+2\pi rh\) where r is the radius of the circular base and h is the height of the cylinder.
Since the diameter of the tank is \(d=36\) ft, then the radius \(r=d\div2=36\div2=18 ft\).
Since we know the surface area is \(S=4750.1 ft^{2}\) and the radius is r=18, we can then substitute these values into the surface area formula to solve for h:
\(S= 2\pi r^{2}+2\pi\ rh\ \text{Surface are formula.}\)
\(4750.1= 2\pi(18)^{2}+2\pi(18)h\ \text{Substitute S}= 4750.1\ and\ r=18.\) \(4750.1= 2\pi(324)+36\pi h\ \text{Simplify.}\) \(4750.1= 648\pi+36\pi h\ \text{Simplify.}\) \(4750.1-648\pi= 36\pi \ Substract\ 648\pi\ on\ both\ sides.\) \((4750.1-648\pi)/(36\pi)=h\ Divide\ both\ sides\ by\ 36\pi.\) \(24\approx h\ \text{Evaluate using a calculator.}\) The height of the cylinder is then 24 ft.

Not exactly what you’re looking for?
Ask My Question
26
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-03-20
A cylindrical reservoir of diameter 4 feet and height 6 feet ishalf full of water weighing 62.5 lbs/ft3. The work done,in ft-lb, in emptying the water over the top is equal to \(\displaystyle\rho\)
asked 2021-10-22
Given 2 rectangles. Model the area of each using a quadratic function, then evaluate each, considering x=8.
(1st) l=2x+4; h=x+3
(2nd) l=3x-9; h=x+2
asked 2021-04-30
Two oppositely charged but otherwise identical conducting plates of area 2.50 square centimeters are separated by a dielectric 1.80 millimeters thick, with a dielectric constant of K=3.60. The resultant electric field in the dielectric is \(\displaystyle{1.20}\times{10}^{{6}}\) volts per meter.
Compute the magnitude of the charge per unit area \(\displaystyle\sigma\) on the conducting plate.
\(\displaystyle\sigma={\frac{{{c}}}{{{m}^{{2}}}}}\)
Compute the magnitude of the charge per unit area \(\displaystyle\sigma_{{1}}\) on the surfaces of the dielectric.
\(\displaystyle\sigma_{{1}}={\frac{{{c}}}{{{m}^{{2}}}}}\)
Find the total electric-field energy U stored in the capacitor.
u=J
asked 2021-12-10
In parallelogram PQSR, what is PQ?
\(\displaystyle{\left({2}{x}+{5}\right)}{c}{m}\)
a) 2 cm
b) 5 cm
c) 6 cm
d) 9 cm
asked 2021-11-22
A paper cup has the shape of a cone with height 10 cm and radius 3 cm (at the top). If water is poured into the cup at a rate of 2 cm^3/s, how fast is the water level rising when the water is 5 cm deep?
asked 2021-06-10
Water flows through a water hose at a rate of \(Q_{1}=680cm^{3}/s\), the diameter of the hose is \(d_{1}=2.2cm\). A nozzle is attached to the water hose. The water leaves the nozzle at a velocity of \(v_{2}=9.2m/s\).
a) Enter an expression for the cross-sectional area of the hose, \(A_{1}\), in terms of its diameter, \(d_{1}\)
b) Calculate the numerical value of \(A_{1},\) in square centimeters.
c) Enter an expression for the speed of the water in the hose, \(v_{1}\), in terms of the volume floe rate \(Q_{1}\) and cross-sectional area \(A_{1}\)
d) Calculate the speed of the water in the hose, \(v_{1}\) in meters per second.
e) Enter an expression for the cross-sectional area of the nozzle, \(A_{2}\), in terms of \(v_{1},v_{2}\) and \(A_{1}\)
f) Calculate the cross-sectional area of the nozzle, \(A_{2}\) in square centimeters.
asked 2021-12-09
A light wave has a 670 nm wavelength in air. Its wavelength in a transparent solid is 420 nm.
a. What is the speed of light in this solid?
b. What is the light’s frequency in the solid?
...