calculus: related rates

hello, please help me.

A cylindrical can is being heated with its height increasing at the rate of 0.01cm/min and its diameter at the rate of 0.005cm/min. At what rate is the volume increasing when the can has a diameter of 15cm and a height of 20cm.

this is how i'm going about the question. I have to find dv/dt. my known variables (i think) are dh/dt=0.01 and ddiam/dt=0.005. and i'm using the equation V=(pi)r^2 * h

I've never done a question before where i was given two rates before, can you please tell me how to go about this question? the solution is 4.123~cm^3/min

and just a little side question. let's say i'm given the rate for the increasing diameter. (as in the question is 0.005cm/min) can i divide that by 2 to get the rate of increasing radius?

Thank you so much for your time

  1. 👍 0
  2. 👎 0
  3. 👁 150
asked by mary
  1. V= PI r^2 * h

    dv/dt= PI (2rh dr/dt+ r^2 dh/dt)

    you are given dh/dt, dr/dt. Find dv/dt when those are given, and given r and h.

  2. :O Thank you so much, for some reason i totally forgot about the product rule! hahah... :)

    1. 👍 0
    2. 👎 0
    posted by mary

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    The flask consist of a cylindrical part and a frustum of a cone. The diameter of the base is 10 cm the diameter is 2 cm while that of neck is 2 cm. The vertical height of the flask is 12 cm. (a) the slant height of the frustum

    asked by K on April 4, 2018
  2. Calculus

    An upright cylindrical tank with radius 3 m is being filled with water at a rate of 4 m3/min. How fast is the height of the water increasing?

    asked by Hector on August 1, 2017
  3. math

    a right circular cylindrical container ,contains 2160cubic cm water. if the diameter of the base of the cylindrical container is 24 cm, then find the height of the cylindrical container.

    asked by akash on September 3, 2017
  4. maths

    A cylindrical can of volume 198cm has a height of 7cm. find the radius of the cylindrical

    asked by Nita on April 5, 2016
  5. Calculus

    The side of a square box is increasing at a rate of 4mm/s and its height is increasing at a rate of 2mm/s. How fast is the volume increasing when the side is 40mm and the height is 100mm. Can someone just tell me what formula to

    asked by Greg on October 18, 2012
  1. calculus

    Previously asked: the length of a rectangular prism is increasing at a rate of 8 cm/s, its width is increasing at a rate of 3 cm/s, and its height is increasing at a rate of 5 cm/s. when the length is 20 cm, width is 10 cm, and

    asked by Dani on December 7, 2014
  2. math

    A cylindrical jar with height 8 inches and diameter 6 inches is filled to 75% capacity with juice. The juice is then poured into another cylindrical container with a 10 inch diameter and height of 4 inches. a. to what percent of

    asked by Phillip on February 25, 2010
  3. Math

    A solid S is made up of a cylindrical part and conical part. The height of the Soild is 4.5m. The common radius of the cylindrical part and the conical part is 0.9m. The height of the conical part is 1.4m. c. A square base pillar

    asked by Kd on September 5, 2018
  4. maths --plse help me..

    A toy is in the shape of a right circular cylinder with hemisphere on one end and a cone on the other . The height and radius of the cylindrical part are 13 cm and 5 cm respectively. The radius of the hemispherical and conical

    asked by sarika on December 4, 2012
  5. maths --Surface area and all that..

    A toy is in the shape of a right circular cylinder with hemisphere on one end and a cone on the other . The height and radius of the cylindrical part are 13 cm and 5 cm respectively. The radius of the hemispherical and conical

    asked by manraj on December 4, 2012

More Similar Questions