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.

Result

r =  8.9 cm

Solution:

a=8 cm h=5 cm  r2=a2+(rh)2 r2=a2+r22rh+h2 2rh=a2+h2  r=a2+h22 h=82+522 5=8910=8.9 cma=8 \ \text{cm} \ \\ h=5 \ \text{cm} \ \\ \ \\ r^2=a^2 + (r-h)^2 \ \\ r^2=a^2 + r^2-2rh + h^2 \ \\ 2rh=a^2 + h^2 \ \\ \ \\ r=\dfrac{ a^2 + h^2 }{ 2 \cdot \ h }=\dfrac{ 8^2 + 5^2 }{ 2 \cdot \ 5 }=\dfrac{ 89 }{ 10 }=8.9 \ \text{cm}



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!
avatar




Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

 

 

 

 

Next similar math problems:

  1. Isosceles triangle
    triangle2_3 The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z.
  2. 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.
  3. Euclid 5
    euclid_3 Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
  4. 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.
  5. RT triangle and height
    345 Calculate the remaining sides of the right triangle if we know side b = 4 cm long and height to side c h = 2.4 cm.
  6. Spruce height
    stromcek_7 How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree?
  7. Double ladder
    rr_rebrik The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
  8. Median in right triangle
    rt_triangle In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse).
  9. Triangle IRT
    triangles_5 In isosceles right triangle ABC with right angle at vertex C is coordinates: A (-1, 2); C (-5, -2) Calculate the length of segment AB.
  10. ABS CN
    complex_num Calculate the absolute value of complex number -15-29i.
  11. Calculate
    equilateral_triangle2 Calculate the length of a side of the equilateral triangle with an area of 50cm2.
  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. 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?
  14. Right 24
    euclid_theorem Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 unequal segments. The length of one segment is 5 cm. What is the area of the triangle? Thank you.
  15. A truck
    truck_11 A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
  16. Triangle ABC
    lalala In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
  17. Double ladder
    dvojak The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?