A cylinder and a cone have the same volume. The cylinder has radius x and height y . The cone has radius 3x . Find

Question

A cylinder and a cone have the same volume. The cylinder has radius x
and height y
. The cone has radius 3x
. Find the height of the cone in terms of y
.

in progress 0
Sadie 1 week 2021-09-10T17:53:54+00:00 2 Answers 0

Answers ( )

    0
    2021-09-10T17:55:02+00:00

    The height of the cone in terms of y would be

    H=4y/3
    SEE WORK BELOW:

    V=∏x2y
    cone
    V=(1/3)∏(3x/2)2H where H=height of the cone
    solve for H
    set the volumes equal to each other
    ∏x2y=(1/3)∏(3x/2)2H
    divide both sides by ∏
    x2y=(1/3)(3x/2)2H
    x2y=(1/3)(9×2/4)H
    x2y=(3×2/4)H
    x2y=(3/4)x2H
    divide both sides by x2
    y=(3/4)H
    multiply both sides by (4/3)
    (4/3)y=H
    H=4y/3 or H=(4/3)y, either way, is the height of the cone

    0
    2021-09-10T17:55:49+00:00

    Answer: h = \frac{y}{3}

    Step-by-step explanation:

    The formula for calculating the volume of a cylinder is given as :

    V = \pi r^{2}h

    The formula for calculating the volume of a cone is given as :

    V = \frac{1}{3}\pi  r^{2}h

    Since the cylinder and the cone have the same volume according to the question , we will equate the two formulas, that is:

    \pi r^{2} h=\frac{1}{3}\pi  r^{2}h

    substituting the values of r , we have

    \pi x^{2} y=\frac{1}{3}\pi  (3x)^{2}h

    \pi x^{2} y=\frac{1}{3}\pi (9x^{2} )h

    since \pi x^{2} is common to both sides , it will cancel out , that is

    y = \frac{1}{3}(9)h

    3y = 9h

    divide through by 9

    3y/9 = h

    Therefore , the height of the cone in terms of y is

    h = \frac{y}{3}

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )