Cone

Circular cone of height 15 cm and volume 5699 cm3 is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.

Result

r =  12.7 cm
o =  79.8 cm

Solution:

V=5699 cm3 h=15 cm  V=13 π r02 h  r0=3 Vπ h=3 56993.1416 1519.0476 cm  r=23 r0=23 19.047612.6984=12.7  cm V = 5699 \ cm^3 \ \\ h = 15 \ cm \ \\ \ \\ V = \dfrac{ 1 }{ 3 } \cdot \ \pi \cdot \ r_{ 0 }^2 \cdot \ h \ \\ \ \\ r_{ 0 } = \sqrt{ \dfrac{ 3 \cdot \ V }{ \pi \cdot \ h } } = \sqrt{ \dfrac{ 3 \cdot \ 5699 }{ 3.1416 \cdot \ 15 } } \doteq 19.0476 \ cm \ \\ \ \\ r = \dfrac{ 2 }{ 3 } \cdot \ r_{ 0 } = \dfrac{ 2 }{ 3 } \cdot \ 19.0476 \doteq 12.6984 = 12.7 \ \text { cm }
o=2π r=2 3.1416 12.698479.7965=79.8  cm o = 2 \pi \cdot \ r = 2 \cdot \ 3.1416 \cdot \ 12.6984 \doteq 79.7965 = 79.8 \ \text { cm }







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

Showing 2 comments:
#
Math student
The solution that you give us doesn't make sense.

#
Dr Math
... and what is bad or unclear? What is your solution?

avatar









Need help calculate sum, simplify or multiply fractions? Try our fraction calculator. Do you want to convert length units? Tip: Our volume units converter will help you with the conversion of volume units. See also our trigonometric triangle calculator.

Next similar math problems:

  1. Cone A2V
    popcorn Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
  2. Cylinder and its circumference
    cylinder If the height of a cylinder is 4 times its circumference. What is the volume of the cylinder in terms of its circumference, c?
  3. Secret treasure
    max_cylinder_pyramid Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
  4. Surface of the cylinder
    valec_1 Calculate the surface of the cylinder for which the shell area is Spl = 20 cm2 and the height v = 3.5 cm
  5. Right Δ
    ruler A right triangle has the length of one leg 7 cm and length of the hypotenuse 25 cm. Calculate the height of the triangle.
  6. Cube in a sphere
    cube_in_sphere_1 The cube is inscribed in a sphere with volume 9067 cm3. Determine the length of the edges of a cube.
  7. Body diagonal
    kvadr_diagonal Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm
  8. Faces diagonals
    cuboid_1 If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.2, y=1.7, z=1.45
  9. Rectangular cuboid
    cuboid_1 The rectangular cuboid has a surface area 5334 cm2, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
  10. Voltmeter range
    predradnik We have a voltmeter which in the original set measures voltage to 10V. Calculate the size of the ballast resistor for this voltmeter, if we want to measure the voltage up to 50V. Voltmeter's internal resistance is 2 kiloohm/Volt.
  11. Cuboid face diagonals
    face_diagonals The lengths of the cuboid edges are in the ratio 1: 2: 3. Will the lengths of its diagonals be the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid.
  12. Equation 23
    reciprocal_1 Find value of unknown x in equation: x+3/x+1=5 (problem finding x)
  13. Geography tests
    test On three 150-point geography tests, you earned grades of 88%, 94%, and 90%. The final test is worth 250 points. What percent do you need on the final to earn 93% of the total points on all tests?
  14. Medians in right triangle
    triangle_rt_taznice It is given a right triangle, angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. .. How to calculate the length of the sides?
  15. Two chords
    tetivy Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
  16. An equilateral triangle
    equilateral_triangle The perimeter of an equilateral triangle is 33cm. How long is each side?
  17. Radius of the circle
    circle_axes Calculate the radius of the circle whose length is 107 cm larger than its diameter