A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 3 ft/min. What is the rate in the change of area at the instant that the radius is 27 ft?

Q: A spherical balloon is inflated and its volume increases at a rate of 30 in3 /min. (a). What is the…

A: Given that, The spherical balloon is inflated and its rate of change of volume is; dVdt=30 (in3min)…

Q: The radius of a circle is increasing at a rate of 2 ft/min. At what rate is its area changing when…

A: NOTE: Refresh your page if you can't see any equations. . the area of the circle is given by  take…

Q: A baseball diamond is a square 90 ft on a side. A player runs from first base to second base at 15…

A: 6)

Q: A thin sheet of ice is in the form of a circle. If the ice is melting, at what rate is the radius…

A: Given a thin sheet of ice is in the form of a circle. And the area is 12 square inches.Let the area…

Q: A conical shaped heap of sand is growing (picture sand being added from above at its peak). If the…

A:

Q: A cylindrical box has a fixed height of 12 inches. Find the rate of change of volume with respect to…

A:

Q: The radius r of a right circular cylinder with a fixed height of 48 inches is increasing. Find the…

A:

Q: Find the rate at which the surface area of the water changes when the water is 10 ft high if the…

A:

Q: if the base of triangle is constantly 4 cm find the rate at which the area of the triangle is…

A:

Q: If the rate change of the length of the circle circumference with time is (T/2) m/sec. What is the…

A:

Q: If the radius of a circle increases at the rate of 0.01 inch/sec, find the rate of change of the…

A: We have, Radius of circle (r)=3 inchesRate of change of radiusdrdt=0.01 inches/sec We know that,…

Q: The radius r of a circle is changing at the rate of -2/π m/sec. At what rate is the circle’s area…

A:

Q: A large weather balloon is being inflated with air at the rate of 0.9 ft3 per minute. Find the rate…

A: Given a large weather balloon is being inflated with air at the rate of 0.9 ft3 per minute. Volume…

Q: The radius of a circle is increasing at the rate of 4 cm/s. How fast is the area of the circle…

A: Given,           The radius of a circle is increasing at the rate of 4 cm/s. And the radius is 5 cm…

Q: A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 4 ft/min.…

A: Area of a circle of radius r is given by  A = πr2                ...(1) Differentiate with respect…

Q: A baseball diamond is a square 90 ft on a side. A player runs from first base to second base at 15…

A:

Q: If the rate of change of the surface area of a sphere with respect to its radius is 16pi sq cm, find…

A:

Q: An inverted conical water tank with a height of 12ft and a radius of 6ft ft is drained through a…

A:

Q: As a circular metal griddle is being heated, its diameter changes at a rate of 0.01 cm/min. Find the…

A:

Q: A spherical balloon is being inflated at the rate of 12m3 /min. If the radius of the balloon is 6m,…

A:

Q: A car is slowing down at the rate 0.8 ft/sec². How far will the car move before it stops if its…

A:

Q: A snowball is melting at a rate of 2.4ft^3 hr^-1 – if the snowball remains a sphere throughout the…

A: given: A snowball is melting at a rate of 2.4ft3/hr. that implies dVdt=-2.4ft3/hr where V is the…

Q: The radius of a circle is increasing at the rate of 0.7 cm/s. what is the rate of

A:

Q: The radius of a circle is increasing at the rate of 0.7 cm/c.what isthe rate of oncreasing of its…

A: Differentiate circumference wrt t

Q: An oil tanker aground on a reef is forming a circular oil slick about 0.1 foot thick. If the oil was…

A: Given that  An oil tanker aground on a reef is forming a circular oil slick about 0.1 foot thick. If…

Q: find the rate of change of the circumference of a circle when the area is increasing at the rate of…

A:

Q: The radius of a sphere decreases at a rate of 3 meters per second. Find the rate at which the…

A:

Q: 16. If the radius of a circle is increasing at the rate of 4 cm/s, find the rate of the increase in…

A: Given radius of a circle is increasing at the rate of 4 cm/sec.

Q: A cylindrical box has a fixed height of 12 inches. Find the rate of change of volume with respect to…

A:

Q: A conical tank that is 14 ft across the entire top and 12 ft deep is leaking water. The radius of…

A:

Q: The radius of a circle is increasing at a rate of 5 centimeters per minute. Find the rate of change…

A: We can find the answer as below using the given data.

Q: The area of a circle increases at a rate of 6 cm /s. a. How fast is the radius changing when the…

A: Area of circle of radius r inA=πr2→dAdr=2πrdrdt→2πrdrdt=6      [∵dAdr=6cm2/sec]    -(1)

Q: Show that the rate of change of the area of a circle with respect to its radius is equal to the…

A: Our Aim is to show that the rate of change of area of a circle with respectto its radius is equal…

Q: A circle has an initial radius of 50 ft. when the radius begins decreasing at the rate of 3 ft/min.…

A: Area of a circle is given byDifferentiating the function of area with respect to time:

Q: A circle has an initial radius of 50 ft when the radius begins decreasing at a rate of 2 ft>min.…

A: Let r be the radius of the circle.The initial radius is given by r = 50 ft.Given that, the radius…

Q: A yellow balloon, spherical in shape is inflated with a rate of 100 cm3 /sec. Calculate the rate at…

A: Given

Q: A funnel in the shape of an inverted cone is 30 cm deep and has a diameter across the top of 20 cm.…

A: Geometry

Q: The area of a circle increases at a rate of 6 cm /s. a. How fast is the radius changing when the…

A:

Q: A cube's volume increases at a rate of 108 ft3/min. At what rate is the cube's edge length changing…

A:

Q: Find the rate of change of the ice circle's area towards the start of spring if the initial radius…

A:

Q: (2) In calm waters, the oil spilling from the ruptured hull of a grounded tanker spreads in all…

A:

Q: A conical cistern of height 5 ft and 7 ft across the top is being filled at a rate of 5 ft3/s while…

A: A conical cistern is given whose height is 5 ft and diameter at the top is 7 ft. A conical cistern…

Q: an oil spill is spreading in a circle at a rate of 316.7in/sec2. at what rate is the radius changing…

A:

Q: 7. A vertical cylinder is leaking water at a rate of 1 ft'/sec. If the cylinder has a height of 10…

A: To find the rate of change of height of water changing

Q: A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 5 ​ft/min.…

A: Given information:

Q: Find the rate of change of the surface area of a hemisphere with respect to its radius. a. When the…

A:

Q: A spherical droplet of water evaporates at a rate of 1 mm3/minute. Find the rate of change of the…

A:

Q: 2) In calm waters, the oil spilling from the ruptured hull of a grounded tanker spreads in all…

A: Solution

Q: If the area of a circle decreases constantly by half a square foot per second, at what rate is its…

A: Here, given that the area of the circle decreases constantly by half s square foot per second. That…