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.

  1. 👍
  2. 👎
  3. 👁
  1. the the radius of the cylinder by x and the height of the cylinder be y.
    (the h and r will be constants)

    by ratios : x/(h-y) = r/h
    y = (hr - hx)/r

    I will assume that you want both top and bottom of the cylinder included in your surface area, if not you will have to change the equation.

    SA = 2πx^2 +2πxy
    = 2πx^2 + 2πhx - (2πh/r)x^2 after subbing in the above y

    SA' = 4πx + 2πh - (4πh/r)x
    = 0 for a max/min of SA

    I get x = hr/(2h-2r)

    put that back into SA = ....

    I will let you finish the algebra.

    (Also check my steps, I tend to make typing errors)

    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. math

    Two right circular cone, one upside down in the other. The two bases are parallel. The vertex of the smaller cone lies at the center of the larger cone’s base. The larger cone’s height and base radius are 12 and 16 ft,

  4. 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?

  1. Calculus

    Given a right circular cone, you put an upside-down cone inside it so that its vertex is at the center of the base of the larger cone, and its base is parallel to the base of the larger cone. If you choose the upside-down cone to

  2. geometry

    A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the

  3. Calculus

    Calculate the height of a cylinder of maximum volume that can be cut from a cone of height 20 cm and base radius 80 cm , please help me

  4. math

    A cone has a radius of 6 inches and a height of 9 inches a) calculate the volume of the cone. use pi. as my answer for part a i got 339.92 cubic inches,,,,,,, Is my answer correct ?? I need help doing part b and c. b) calculate a

  1. ALGEBRA 2 HONORS

    A container is to be made in the shape of a cylinder with a conical top. The lateral surface areas of the cylinder and cone are S1 = 2(pi)rh and S2 = 2(pi)r√(r^2 + h^2). The surface area of the base of the container is B=

  2. 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

  3. MATH QUIZ PLS HELP!!!

    1.Find the lateral area of a cone with a radius of 7 ft. and a slant height of 13 ft. Use 3.14 for ©£ and round to the nearest tenth. 439.6 ft^2 324.5 ft^2 571.5 ft^2 285.7 ft^2*** 2.Find the surface area of a square pyramid

  4. Math

    1.) find the volume of the given pyramid. H= 7yd B= 7yd and L= 9yd A. 147yd.^3 B. 157 yd.^3 C. 221 yd.^3 D. 441 yd.^3 ******* 2. Find the volume of a square pyramid with a base length of 9 cm and a height of 4cm. A. 324cm. ^3 B.

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