Home -> Solved problems -> Volume of kiln

Volume of kiln


Let \(x>0\)
\[\begin{aligned} 3-\cosh x =0 \\\\ \cosh x =3 \\\\ x= \ln (3+2 \sqrt{2}) \end{aligned}\]
\[\begin{gathered} v^{*}=\{(x, y, z): 0 \leqslant x \leqslant \ln (3+2 \sqrt{2}),\;\;\; 0 \leqslant y \leqslant 3-\cosh x ,\;\;\; 0 \leqslant z \leqslant 6\} \end{gathered}\]
\[v=2 v^{*}\]
\[v=2 \iiint_{v} d v \] \[=2 \int_{0}^{\operatorname{ln}(3+2 \sqrt{2})} d x \int_{0}^{3-\cosh x} d y \int_{0}^{6} d z \] \[=2 \int_{0}^{\ln(3+2 \sqrt{2})} d x \int_{0}^{3-\cosh x}6\; d y \] \[=\left.12 \int_{0}^{\ln\left(3+2\sqrt{2}\right)} y\right|_{0} ^{3-\cosh x} d x \] \[=12 \int_{0}^{\left.(\ln3+2\sqrt{2}\right)}(3-\cosh x) d x \] \[=12[3 x-\sinh x]_{0}^{\ln (3+2 \sqrt{2})} \] \[=12[3 \ln (3+2 \sqrt{2})-\sinh (\ln (3+2 \sqrt{2}))] \]
\[\cong 29,5178 \ldots \]
Home -> Solved problems -> Volume of kiln

Every problem you tackle makes you smarter.

↓ Scroll down for more maths problems↓

How Tall Is The Table ?
How far apart are the poles ?
Determine the square's side \(x\)
Find the volume of the interior of the kiln
Solve the equation for real values of \(x\)
Find the equation of the curve formed by a cable suspended between two points at the same height
Why 0.9999999...=1
Calculate the integral
Error to avoid that leads to:
What's the problem ?
Explain your answer without using calculator
Calculate the sum of areas of the three squares
What values of \(x\) satisfy this inequality
Prove that the function \(f(x)=\frac{x^{3}+2 x^{2}+3 x+4}{x} \) has a curvilinear asymptote \(y=x^{2}+2 x+3\)
Why does the number \(98\) disappear when writing the decimal expansion of \(\frac{1}{9801}\) ?
Only one in 1000 can solve this math problem
Calculate the following
Find the limit of width and height ratio
Is \(\pi\) an irrational number ?
Solve for \(x \in \mathbb{R}\)
Prove that \(e\) is an irrational number
Prove that
Challenging problem
Solve the equation for \(x \in \mathbb{R}\)
Calculate the following limit
Calculate the following limit
Determine the angle \(x\)
Find the derivative of \(y\) with respect to \(x\)
Prove Wallis Product Using Integration
Calculate the radius R
Calculate the volume of Torus using cylindrical shells
Find the derivative of exponential \(x\) from first principles
Find the volume of the square pyramid as a function of \(a\) and \(H\) by slicing method.
Prove that \[\lim_{x \rightarrow 0}\frac{\sin x}{x}=1\]
Prove that
Calculate the half derivative of \(x\)
Find out what is a discriminant of a quadratic equation.
Calculate the rectangle's area
Infinitely nested radicals
Determine the square's side \(x\)
Wonderful math fact: 12542 x 11 = 137962
Calculate the sum
What is the new distance between the two circles ?
Solve the equation for \(x\epsilon\mathbb{R}\)
Calculate the area of the Squid Game diagram blue part
Calculate the limit
Find the infinite sum
Calculate the integral
Prove that
Can we set up this tent ?
Find the value of \(h\)
Is the walk possible?
Find the length of the black segment
Prove that pi is less than 22/7
Find the value of \(x\)
Amazing !
Prove that
What is the weight of all animals ?
Determine the length \(x\) of the blue segment
How many triangles does the figure contain ?
if we draw an infinite number of circles packed in a square using the method shown below, will the sum of circles areas approach the square's area?
What is the value of the following infinite product?
Which object weighs the same as the four squares?
What is \((-1)^{\pi}\) equal to?
Can you solve it?
Can you solve it?
Great Math Problem
Calculate the integral \(\int_{0}^{1}(-1)^{x} d x\)
Find the general term of the sequence
Find the radius of the blue circles
Determine the area of the green square
Find the area of the square
Calculate the integral
Calculate the integral
What is the radius of the smallest circle ?
Find the Cartesian equation of the surface
Calculate the integral
Calculate the limit
Can you solve this ?
Solve the quintic equation for real \(x\)
How many students study no language ?
Probability of seeing a car in 10 minutes
What is the number of where the car stands ?
What is the value of \(x\) ?