The cylinder

The cylinder has a surface area of 300 square meters, while the height of the cylinder is 12 m. Calculate the volume of this cylinder.

Correct result:

V =  374.381 m³

Solution:

$$\begin{gathered} S=300{\text{m}}^2 \\ h=12\text{ cm } \\ S=2\ast pi\ast r^2+2\ast pi\ast r\ast h \\ 300=2\cdot 3.1415926\cdot r^2+2\cdot 3.1415926\cdot r\cdot 12 \\ -6.2831852r^2-75.398r+300=0 \\ 6.2831852r^2+75.398r-300=0 \\ a=6.2831852;b=75.398;c=-300 \\ D=b^2-4ac=75.398^2-4\cdot 6.2831852\cdot (-300)=13224.7141811 \\ D>0 \\ {r}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{-75.4\pm \sqrt{13224.71}}{12.5663704}} \\ {r}_{1,2}=-6\pm 9.15131049315 \\ {r}_1=3.15131049315 \\ {r}_2=-15.1513104931 \\ \text{ Factored form of the equation: } \\ 6.2831852(r-3.15131049315)(r+15.1513104931)=0 \\ r=r_1=3.1513\doteq 3.1513 \\ {S}_1=\pi \cdot r^2=3.1416\cdot 3.1513^2\doteq 31.1984{\text{m}}^2 \\ V=S_1\cdot h=31.1984\cdot 12\doteq 374.3807\doteq 374.381{\text{m}}^3 \\ \text{ Correctness test: } \\ {S}_2=2\pi \cdot r^2+2\pi \cdot r\cdot h=2\cdot 3.1416\cdot 3.1513^2+2\cdot 3.1416\cdot 3.1513\cdot 12=300 \\ S=S_2 \end{gathered}$$

Checkout calculation with our calculator of quadratic equations.

Try another example

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:

Next similar math problems:

• Shell area cy
  The cylinder has a shell content of 300 cm square, while the height of the cylinder is 12 cm. Calculate the volume of this cylinder.
• Volume and surface
  Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm².
• Rotary cylinder 2
  Base circumference of the rotary cylinder has same length as its height. What is the surface area of cylinder if its volume is 250 dm³?
• Cylinder diameter
  The surface of the cylinder is 149 cm². The cylinder height is 6 cm. What is the diameter of this cylinder?
• Cylinder - A&V
  The cylinder has a volume 1287. The base has a radius 10. What is the area of surface of the cylinder?
• Square root 2
  If the square root of 3m² +22 and -x = 0, and x=7, what is m?
• Roots
  Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
• Discriminant
  Determine the discriminant of the equation: ?
• Holidays - on pool
  Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
• The product
  The product of a number plus that number and its inverse is two and one-half. What is the inverse of this number
• Expression with powers
  If x-1/x=5, find the value of x⁴+1/x⁴
• Equation
  Equation ? has one root x₁ = 8. Determine the coefficient b and the second root x₂.
• Equation 23
  Find value of unknown x in equation: x+3/x+1=5 (problem finding x)
• Quadratic equation
  Find the roots of the quadratic equation: 3x²-4x + (-4) = 0.
• Solve 3
  Solve quadratic equation: (6n+1) (4n-1) = 3n²
• Algebra
  X+y=5, find xy (find the product of x and y if x+y = 5)
• Evaluation of expressions
  If a²-3a+1=0, find (i)a²+1/a² (ii) a³+1/a³