Find the moment of inertia of a right circular cylinder of radius of base R and height H, about the axis of the cylinder, if the density at the point P is proportional to the distance from P to the axis of the cylinder. Write down the resultin terms of the mass of the cylinder.
did I do this right and do you think my answer correct?

formulais I/m=R, denisty=kr
I = I= [0,R]∫[0,H]∫[0,2]∫𝑟^2(kr)rdzdrd𝜃=> (2𝜋)k(𝑅^3 /3)H = (2𝜋Hk𝑅^3)/3
I = m= [0,R]∫[0,H]∫[0,2]∫(kr)rdzdrd𝜃=> (2𝜋)k(𝑅)H = 2𝜋Hk𝑅
R=I/m=>R= ((2𝜋Hk𝑅^3)/3)/(2𝜋Hk𝑅)=answer R^2

  1. 👍
  2. 👎
  3. 👁
  1. As I recall, the moment of inertia is
    ∫∫∫ r^2 p dv
    which in this case would indeed be
    ∫∫∫ r^2 * kr dv
    and dv = r dr dθ dz
    so it looks like you're good to go, except you dropped that extra r. See it hiding there in your original integrand?

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    Find the maximum volume of right circular cylinder that can be inscribed in a cone of altitude 12 cm and base radius 4 cm, if the axes of the cylinder and con coincide.

  2. Math

    The volume of a cylinder is given by formula V= pi(3.14) r^2h where r is base radius and h is height a) the height of a cylinder of radius 5cm and volume 500. Cm^3 B) radius of base of a cylinder of volume 300 cm^3 and height 10

  3. Calculus

    A cylinder is inscribed in a right circular cone of height 5.5 and radius (at the base) equal to 2 . A) What are the dimensions of such a cylinder which has maximum volume? B) What is the radius? C) What is the height?

  4. differential calculus

    a right circular cylinder has a fixed height of 6 units. Find the ratio of change of its volume(v) with respect to the radius(r) of its base.

  1. 4 Calculus Related-Rates Problems

    1. How fast does the radius of a spherical soap bubble change when you blow air into it at the rate of 15 cubic centimeters per second? Our known rate is dV/dt, the change in volume with respect to time, which is 15 cubic

  2. math

    A container in the shape of a right circular cylinder with no top has surface area 3*pi (m2). What height h and base radius r will maximize the volume of the cylinder ?

  3. Maths

    A metallic right circular cylinder is15cm high and the diameter of the base is 14cm it is melted and recasted into another cylinder with radius 4cm find its height and curved surface area

  4. Algebra

    The volume of a right circular cylinder (think of a pop can) is jointly proportional to the square of the radius of the circular base and to the height. For example, when the height is 10.62 cm and the radius is 3 cm, then the

  1. astronomy

    Rank the following hypothetical planets -- all of which have the same total mass and same radius -- from lowest moment of inertia to highest moment of inertia: 1) A uniform sphere of mixed up rock and iron 2) A rocky planet with

  2. Physics

    M, a solid cylinder (M=2.35 kg, R=0.111 m) pivots on a thin, fixed, frictionless bearing. A string wrapped around the cylinder pulls downward with a force F which equals the weight of a 0.750 kg mass, i.e., F = 7.357 N.

  3. math

    A cylinder has a circular base with a diameter of 12 ft. The height of the cylinder is 4 ft. What is the volume of the cylinder rounded to the nearest whole number? Use 3.14 for pi.

  4. Calculus

    A right circular cylinder is inscribed in a cone with height h and base radius r. Find the largest possible surface area of such a cylinder.

You can view more similar questions or ask a new question.