Sphere - parts

Calculate the area of a spherical cap, which is part of an area with base radius ρ = 9 cm and a height v = 3.1 cm.

Correct answer:

S =  697.88 cm²

Step-by-step explanation:

$$\begin{gathered} r^2={\rho }^2+(r-v{)}^2 \\ {r}^2={\rho }^2+r^2-2rv+v^2 \\ 2rv={\rho }^2+v^2 \\ r={\displaystyle \frac{9^2+3.1^2}{2\cdot 3.1}}=14.61cm \\ S=\pi r\rho +2\pi rv=\pi r(\rho +2v)=697.88{\text{cm}}^2 \end{gathered}$$

Try another example

Related math problems and questions:

• Spherical cap
  Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm². Determine the radius r of the sphere from which the spherical cap was cut.
• Spherical cap
  The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut.
• Spherical cap
  From the sphere of radius 11 was truncated spherical cap. Its height is 6. What part of the volume is a spherical cap from the whole sphere?
• Spherical cap 4
  What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula.
• A spherical segment
  A spherical section whose axial section has an angle of j = 120° in the center of the sphere is part of a sphere with a radius r = 10 cm. Calculate the cut surface.
• Spherical cap
  What is the surface area of a spherical cap, the base diameter 20 m, height 2 m.
• Sphere parts, segment
  A sphere with a diameter of 20.6 cm, the cut is a circle with a diameter of 16.2 cm. .What are the volume of the segment and the surface of the segment?
• Above Earth
  To what height must a boy be raised above the earth to see one-fifth of its surface.
• Spherical segment
  The spherical segment with height h=1 has a volume V=223. Calculate the radius of the sphere of which is cut this segment.
• Airplane
  Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
• Spherical segment
  Calculate the volume of a spherical segment 18 cm high. The diameter of the lower base is 80 cm, the upper base 60 cm.
• 9-gon pyramid
  Calculate the volume and the surface of a nine-sided pyramid, the base of which can be inscribed with a circle with radius ρ = 7.2 cm and whose side edge s = 10.9 cm.
• 3sides prism
  The base of vertical prism is an isosceles triangle whose base is 10 cm and the arm is 13 cm long. Prism height is three times the height of base triangle. Calculate the surface area of the prism.
• Vertical prism
  The base of the vertical prism is a right triangle with leg a = 5 cm and a hypotenuse c = 13 cm. The height of the prism is equal to the circumference of the base. Calculate the surface area and volume of the prism
• Cube from sphere
  What largest surface area (in cm²) can have a cube that we cut out of a sphere with radius 43 cm?
• The roof
  The roof has the shape of a spherical canopy with a base diameter of 8 m and a height of 2 m, calculate the area of the foil with which the roof is covered, when we calculate 13% for waste and residues.
• Elevation
  What must be the elevation of an observer in order that he may be able to see an object on the earth 536 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.