Calculus

posted by .

Consider a hemispherical bowl of radius 10cm.

(4 points) If the water level in the bowl is h cm deep, find the radius of the surface of the water as a function of h.

(6 points) The water level drops at a rate of 0.1 cm per hour. At what rate is the radius of the water decreasing when the depth is 5 cm?

  • Calculus -

    draw a vertical cross-section of the bowl. Pick a point H on the vertical axis at height h from the bottom. If P is a point on the rim of the bowl, HP = 10. The radius at H is

    (10-h)^2 + r^2 = 10^2
    r = √(100-(10-h)^2)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    A hemispherical bowl with a 30-cm radius has some water in it. The water is 15 cm deep. Find the volume of water, to the nearest cubic cm.
  2. Calculus

    An open hemispherical bowl of radius R is slowly draining through a small hole of radius r in the bottom of the bowl. Let g be the acceleration due to gravity and y be the depth of the water (which means the distance from the water …
  3. Math

    If a hemispherical bowl of radius 6cm contains water to a depth of h cm, the volume of the water is 1/3πh^2(18-h). Water is poured into the bowl at a rate 4 cm^3/s . Find the rate at ehich the water level is rising when the depth …
  4. Geometry

    I need help!!! a hemispherical bowl with radius 25cm contains water whose depth is 10cm. what is the water's surface area
  5. Geometry

    a hemispherical bowl with radius 25cm contains water whose depth is 10cm. what is the water's surface area
  6. Math

    Yan water leaks from a hemispherical bowl of 8 cm diameter at the rate of 10 cm per hour .How fast is the surface falling when the water is 2 cm deep in the bowl
  7. geometry

    The water level in a spherical bowl has a diameter of 30cm. If the horizontal diameter of the bowl is 10cm below the water level. calculate the radius of the bowl and the depth of the water in the bowl.
  8. pope john

    A hemispherical bowl of radius 6cm contains water which is flowing into it at a constant rate.When the height of the water is h cm the volume V of water in the bowl is given by V=22/7(6h^2-1/3h^3)cm^3.Find the rate at which the water …
  9. Calculus

    Water is flowing into a hemispherical bowl having a radius of 10cm at constant rate of 3cm^3/min. When the water is x cm deep, The water level rises at a rate of 0.0149 cm/min. What is the value of x?
  10. Pre-Calculus

    A hemispherical bowl with a 30-centimeter radius contains some water, which is 12 centimeters deep. Find the volume of the water.

More Similar Questions