The surface

The surface of the cylinder is 1570 cm², its height is 15 cm. Find its volume and radius of the base.

Correct answer:

V =  4712.389 cm³
r =  10 cm

Step-by-step explanation:

$$\begin{gathered} S=1570{\text{cm}}^2 \\ h=15\text{ cm } \\ S=2\ast pi\ast r(r+h) \\ 1570=2\cdot 3.1415926\cdot r(r+15) \\ -6.2831852r^2-94.248r+1570=0 \\ 6.2831852r^2+94.248r-1570=0 \\ a=6.2831852;b=94.248;c=-1570 \\ D=b^2-4ac=94.248^2-4\cdot 6.2831852\cdot (-1570)=48341.0467139 \\ D>0 \\ {r}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{-94.25\pm \sqrt{48341.05}}{12.5663704}} \\ {r}_{1,2}=-7.5\pm 17.4963786229 \\ {r}_1=9.99637862292 \\ {r}_2=-24.9963786229 \\ \text{ Factored form of the equation: } \\ 6.2831852(r-9.99637862292)(r+24.9963786229)=0 \\ r=[r_1]=[9.9964]=10\text{ cm } \\ V=\pi \cdot r^2\cdot h=3.1416\cdot 10^2\cdot 15=4712.389{\text{cm}}^3 \end{gathered}$$

Our quadratic equation calculator calculates it.

Try another example

Related math problems and questions:

• Rotary cylinder
  In the rotary cylinder it is given: surface S = 96 cm² and volume V = 192 cm cubic. Calculate its radius and height.
• The cylinder
  In a rotating cylinder it is given: the surface of the shell (without bases) S = 96 cm² and the volume V = 192 cm cubic. Calculate the radius and height of this cylinder.
• 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.
• Cuboid height
  What is the height of the cuboid if the edges of its base are 15 cm and 4 cm long and its volume is 420 cm cubic?
• Truncated pyramid
  The truncated regular quadrilateral pyramid has a volume of 74 cm³, a height v = 6 cm, and an area of the lower base 15 cm² greater than the upper base's content. Calculate the area of the upper base.
• Axial cut of a rectangle
  Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long.
• Cuboid and eq2
  Calculate the volume of cuboid with square base and height 6 cm if the surface area is 48 cm².
• Rhombus base
  Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u₁ = 12 cm and u₂ = 15 cm. Prism height is twice the base edge length.
• Rotary bodies
  The rotating cone and the rotary cylinder have the same volume of 180 cm³ and the same height v = 15 cm. Which of these two bodies has a larger surface area?
• Diameter = height
  The cylinder's surface, the height of which is equal to the diameter of the base, is 4239 cm square. Calculate the cylinder volume.
• Dimensions of the trapezoid
  One of the bases of the trapezoid is one-fifth larger than its height, the second base is 1 cm larger than its height. Find the dimensions of the trapezoid if its area is 115 cm²
• Hexagonal prism 2
  The regular hexagonal prism has a surface of 140 cm² and height of 5 cm. Calculate its volume.
• Cylinder surface, volume
  The area of the cylinder surface and the cylinder jacket are in the ratio 3: 5. The height of the cylinder is 5 cm shorter than the radius of the base. Calculate surface area and volume of the cylinder.
• Hard cone problem
  The surface of the cone is 200 cm², its height is 7 centimeters. Calculate the volume of this cone.
• The cylinder
  The cylinder has a surface area of 300 square meters, while the cylinder's height is 12 m. Calculate the volume of this cylinder.
• Equilateral cylinder
  Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm³ . Calculate the surface area of the cylinder.
• Triangular prism
  The triangular prism has a base in the shape of a right triangle, the legs of which is 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm³? And the surface cm²?