Spherical cap

From the sphere of radius 13 was truncated spherical cap. Its height is 6. What part of the volume is spherical cap from whole sphere?

Correct result:

x =  13.5 %

Solution:

ρ2=132−(13−6)2=120 V1=π⋅66(3⋅ρ2+62)=1244.07 V2=4π3133=9202.77  x=V1V2 x=13.5%\rho^2 = 13^2 - (13-6)^2 = 120 \ \\ V_1 = \dfrac{ \pi\cdot 6}{6} (3\cdot \rho^2+6^2) = 1244.07 \ \\ V_2 = \dfrac{ 4 \pi}{3} 13^3 = 9202.77 \ \\ \ \\ x = \dfrac{ V_1}{ V_2} \ \\ x=13.5 \%

Try another example


We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
avatar




Tips to related online calculators
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Pythagorean theorem is the base for the right triangle calculator.

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1   video2   video3

Next similar math problems:

  • Mom and daughter
    family_1 Mother is 39 years old. Her daughter is 15 years. For many years will mother be four times older than the daughter?
  • Dining room
    table The dining room has 11 tables (six and eight seats). In total there are 78 seats in the dining room. How many are six-and eight-seat tables?
  • Pine
    trees How much of a mixed forest rangers want to cut down, if their head said: "We only cut down pine trees, which in our mixed forest 98%. After cut pine trees constitute 94% of all trees left."
  • Nineteenth member
    seq_sum_1 Find the nineteenth member of the arithmetic sequence: a1=33 d=5 find a19
  • Fifth of the number
    numbs_5 The fifth of the number is by 24 less than that number. What is the number?
  • Boxes
    krabice 200 boxes have been straightened in three rows. The first was 13 more than in the second, and in the second was one fifth more than in the third one. How many boxes are in each row?
  • Competitors
    ski_2 In the first round of slalom fell 15% of all competitors and in the second round another 10 racers. Together, 40% of all competitors fell. What was the total number of competitors?
  • Equation with abs
    abs Solve this equation with absolute value member: ?
  • Pears
    hrusky Andrew, Lenka and Rasto have together 232 pears. Lenka has 28 more than Rasto and Rasto pears have 96 more than Andrew. Determine how much each of them has pears.
  • Sphere growth
    sphere How many times grow volume of sphere if diameter rises 10×?
  • Fraction
    polynomial For what x expression ? equals zero?
  • Glass
    sklenice_1 Trader ordered from the manufacturer 200 cut glass. The manufacturer confirmed the order that the glass in boxes sent a kit containing either four or six glasses. Total sent 41 boxes. a) How many boxes will contain only 4 glasses? b) How many boxes will c
  • Ravens
    havrany On two trees sitting 17 ravens. If 3 ravens flew from first to second tree and 5 ravens took off from second tree then the first tree has 2 times more ravens than second tree. How many ravens was originally on every tree?
  • Mean
    integrales if the mean of the set of data 5, 17, 19, 14, 15, 17, 7, 11, 16, 19, 5, 5, 10, 8, 13, 14, 4, 2, 17, 11, x is -91.74, what is the value of x?
  • Gasholder
    gas_holder The gasholder has spherical shape with a diameter 23 m. How many m3 can hold in?
  • 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?
  • Hollow sphere
    sphere2 The volume of the hollow ball is 3432 cm3. What is its internal radius when the wall thickness is 3 cm?