Into rotating cone with dimensions r = 8 cm and h = 8 cm incribe cylinder with maximum volume so that the cylinder axis is perpendicular to the axis of the cone. Determine the dimensions of the cylinder.

Correct result:

r =  2.67 cm
h =  5.33 cm


V=13πr2h x/R=2r/H  r=H2Rx=828x h=2(Rx)=2(8x)  V=13π(828x)22(8x)  V=π82682(8x2x3)  V=π82682(28x3x2) V=0 28x3x2=0 x1=0 283x=0  16=3x  x=5.333 cm r=8285.333=2.67 cm 
h=2(85.333)=5.33 cm

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:

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

Next similar math problems:

  • Calculation of CN
    color_combinations Calculate: ?
  • Linsys2
    linear_eq_3 Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
  • Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  • The determinant
    matrix_13 The determinant of the unit matrix equals 7. Check how many rows the A matrix contains.
  • Median and modus
    dice_3 Radka made 50 throws with a dice. The table saw fit individual dice's wall frequency: Wall Number: 1 2 3 4 5 6 frequency: 8 7 5 11 6 13 Calculate the modus and median of the wall numbers that Radka fell.
  • Cylinder diameter
    valec.JPG The surface of the cylinder is 149 cm2. The cylinder height is 6 cm. What is the diameter of this cylinder?
  • Inverse matrix
    matrix_3 Find how many times is the larger determinant is the matrix A, which equals 9 as the determinant of its inverse matrix.
  • AS sequence
    AP In an arithmetic sequence is given the difference d = -3 and a71 = 455. a) Determine the value of a62 b) Determine the sum of 71 members.
  • Derivation
    fx Exists a function whose derivation is the same function?
  • Minimum of sum
    derive_1 Find a positive number that the sum of the number and its inverted value was minimal.
  • The shooter
    terc The shooter shoots at the target, assuming that the individual shots are independent of each other and the probability of hitting each of them is 0.2. The shooter fires until he hits the target for the first time, then stop firing. (a) What is the most li
  • Statue
    michelangelo On the pedestal high 4 m is statue 2.7 m high. At what distance from the statue must observer stand to see it in maximum viewing angle? Distance from the eye of the observer from the ground is 1.7 m.
  • Shopping malls
    tv The chain of department stores plans to invest up to 24,000 euros in television advertising. All commercials will be placed on a television station where the broadcast of a 30-second spot costs EUR 1,000 and is watched by 14,000 potential customers, durin
  • Curve and line
    parabol The equation of a curve C is y=2x² -8x+9 and the equation of a line L is x+ y=3 (1) Find the x co-ordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
  • Jar
    sklenice From the cylinder shaped jar after tilting spilled water so that the bottom of the jar reaches the water level accurately into half of the base. Height of jar h = 7 cm and a jar diameter D is 12 cm. How to calculate how much water remains in the jar?
  • Paper box
    box Hard rectangular paper has dimensions of 60 cm and 28 cm. The corners are cut off equal squares and the residue was bent to form an open box. How long must be side of the squares to be the largest volume of the box?
  • Cylindrical container
    valec2_6 An open-topped cylindrical container has a volume of V = 3140 cm3. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container.