Above Earth

To what height must a boy be raised above the earth in order to see one-fifth of its surface.


h =  4252 km


R=6378 km S1=4π R2=4 3.1416 63782511185932.5225 km2 S=1/5 S1=1/5 511185932.5225102237186.5045 km2 S=2πRv v=S/(2π R)=102237186.5045/(2 3.1416 6378)=127565=2551.2 y=Rv=63782551.2=191345=3826.8 x=R2y2=637823826.82=255125=5102.4 k=\cotanα=x/y=(h+v)/x x/y=(h+v)/x h+v=x2/y h=x2/yv=5102.42/3826.82551.2=4252 kmR=6378 \ \text{km} \ \\ S_{1}=4 \pi \cdot \ R^2=4 \cdot \ 3.1416 \cdot \ 6378^2 \doteq 511185932.5225 \ \text{km}^2 \ \\ S=1/5 \cdot \ S_{1}=1/5 \cdot \ 511185932.5225 \doteq 102237186.5045 \ \text{km}^2 \ \\ S=2 \pi R v \ \\ v=S / (2 \pi \cdot \ R)=102237186.5045 / (2 \cdot \ 3.1416 \cdot \ 6378)=\dfrac{ 12756 }{ 5 }=2551.2 \ \\ y=R - v=6378 - 2551.2=\dfrac{ 19134 }{ 5 }=3826.8 \ \\ x=\sqrt{ R^2-y^2 }=\sqrt{ 6378^2-3826.8^2 }=\dfrac{ 25512 }{ 5 }=5102.4 \ \\ k=\cotan \alpha=x/y=(h+v)/x \ \\ x/y=(h+v)/x \ \\ h+v=x^2/y \ \\ h=x^2/y - v=5102.4^2/3826.8 - 2551.2=4252 \ \text{km}

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!

Tips to related online calculators
Need help calculate sum, simplify or multiply fractions? Try our fraction calculator.
Pythagorean theorem is the base for the right triangle calculator.

Next similar math problems:

  1. Spherical cap 4
    spherical cap What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula.
  2. Spherical cap
    koule2 What is the surface area of a spherical cap, the base diameter 20 m, height 2 m.
  3. Fit ball
    fitball What is the size of the surface of Gymball (FIT - ball) with a diameter of 65 cm?
  4. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  5. Sphere cuts
    sphere_cut At what distance from the center intersects sphere with radius R = 56 plane, if the cut area and area of the main sphere circle is in ratio 1/2.
  6. Castle tower
    veza The castle tower has a cone-shaped roof with a diameter of 10 meters and a height of 8 meters. Calculate how much m² of coverage is needed to cover it if we must add one-third for the overlap.
  7. Sphere - parts
    odsek_vusek 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.
  8. Hemispherical hollow
    odsek The vessel hemispherical hollow is filled with water to a height of 10 cm =. How many liters of water are inside if the inside diameter of the hollow is d = 28cm?
  9. Euclid2
    euclid In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
  10. Spherical cap
    gulovy_odsek 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.
  11. Observatory
    kopula Observatory dome has the shape of a hemisphere with a diameter d = 16 m. Calculate the surface.
  12. Holidays - on pool
    pool_4 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?
  13. Coefficient
    gp Determine the coefficient of this sequence: 7.2; 2.4; 0.8
  14. ABS CN
    complex_num Calculate the absolute value of complex number -15-29i.
  15. Vector 7
    vectors_sum0_1 Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
  16. Expression with powers
    eq222_9 If x-1/x=5, find the value of x4+1/x4
  17. Algebra
    parabol_3 X+y=5, find xy (find the product of x and y if x+y = 5)