# 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.

Result

v =  1.384 cm
r =  2.684 cm

#### Solution:

$D=4.6 \ \text{cm} \ \\ r_{ 1 }=D/2=4.6/2=\dfrac{ 23 }{ 10 }=2.3 \ \text{cm} \ \\ S=20 \ \text{cm}^2 \ \\ \ \\ S=2 \ \pi r_{ 1 } . v \ \\ v=\dfrac{ S }{ 2 \pi \cdot \ r_{ 1 } }=\dfrac{ 20 }{ 2 \cdot \ 3.1416 \cdot \ 2.3 } \doteq 1.384 \doteq 1.384 \ \text{cm}$
$r^2=r_{ 1 }^2 + v^2 \ \\ r=\sqrt{ r_{ 1 }^2+v^2 }=\sqrt{ 2.3^2+1.384^2 } \doteq 2.6843 \doteq 2.684 \ \text{cm}$

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...):

Be the first to comment!

Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.

## Next similar math problems:

1. Hemispherical hollow
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?
2. Sphere cuts
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. Spruce height
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?
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?
5. 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?
6. Theorem prove
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?
7. Isosceles triangle
The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z.
8. Median
In triangle ABC is given side a=10 cm and median ta= 13 cm and angle gamma 90°. Calculate length of the median tb.
9. Right 24
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.
10. Euclid 5
Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
11. Triangle IRT
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.
12. Median in right 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).
13. A truck
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)?