A cylindrical water tank has a height of 20ft and a radius of 6ft. the tank is leaking water at the rate of 3 cubic feet per hour. Find the rate of change in the height of the water when it is 15ft deep. Explain what this means. V = ar²h

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: B. How rapidly will the water level inside a vertical cylindrical tank if we pump the water out at…

A:

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: An engineer is experimenting with a cylindrical can with a fixed height of 15 in. Find the rate of…

A: GIVEN-  A CYLINDER OF HEIGHTS 15 inch is given AND RADIUS =4 inch TO FIND -  RATE OF CHANGE OF…

Q: The radius of a sphere decreases at a rate of 1 m/se decreases when the radius is 15 m

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 side of a cube is increasing at a rate of 5cm/sec, find the related change in surface area wher…

A:

Q: Gas is being pumped into a spherical balloon at the rate of 10 cubic inches per second. When the…

A: we have given that Gas is being pumped into a spherical balloon at the rate of 10 cubicinches per…

Q: A spherical balloon is inflated with air at a rate of 32 cm3/ min. At what rate does the radius…

A: Find dr/dr.

Q: Find the rate at which the water level is rising when the water level is 2 cm.

A:

Q: The volume of a sphere is increasing at a rate of 4 cm3/sec. Find the rate of change of its surface…

A: We will use derivative as rate of change

Q: The side of a cube decreases at a rate of 8 m/sec. Find the rate at which the volume changes, when…

A: given that a side of cubedecreases at a rate of 8m/sfind the rate at which the volume changes when…

Q: At what rate is water pouring into a rectangular bathtub with base 65 fť if the water level rises at…

A: According to the given information it is required to calculate the rate at which water is pouring…

Q: Water is flowing into a (inverted) conical reservoir 20 feet and 10 feet across the top, at the rate…

A:

Q: A woman is flying a kite on a long string. The kite itself has a 150 ft above the ground of the wind…

A: In the question we have to find the rate of string to let out.

Q: An engineering student is experimenting on a cylindrical can with a fixed rate of 8 inches. Find the…

A:

Q: Water is flowing into a conical reservoir 20 ft. deep and 10 ft. diameter across the top, at the…

A:

Q: Rain is falling into a cylindrical barrel at the rate of 20 cm3/min. If the radius of the base is 18…

A: Given,            Rain is falling into a cylindrical barrel at the rate of 20 cm3/min.…

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: Consider a pool shaped like the bottom half of a sphere, that is being filled. The radius of the…

A: The volume of hemisphere filled with liquid to height h = πrh2-π3h3

Q: A large conical tank of height H being filled with water by a hose at the top of the tank at a rate…

A: given: A large conical tank of height H=9 feet and radius R=3 feet is being filled with water by a…

Q: Find the rate of change of the total surface area of a cylinder of radius r and height h, when the…

A:

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: Water is flowing into an inverted conical reservoir, 20 ft deep and 10 ft across the top, at the…

A:

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

A:

Q: The side of a cube decreases at a rate of 7 m/sec. Find the rate at which the volume changes, when…

A:

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

A:

Q: A piston is seated at the top of a cylindricalchamber with radius 5 cm when itstarts moving into the…

A: From the given data:

Q: Rain is falling into a cylindrical barrel at the rate of 20 cm3 /min. If the radius of the base is…

A:

Q: The legs of an isosceles right triangle increase in length at a rate of 6 m divided by s.a. At what…

A: Let x  be the length of leg and h be the length of hypotenuse of an isosceles right triangle. Then…

Q: A Fluid flows in an inverted conical tank, 14 in diameter on top and 24in deep at a rate of…

A:

Q: A boy is blowing a spherical balloon at a rate of 50cm3/s. At what rate is the radius of the balloon…

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 height h of a right circular cylinder is twice its radius r. Find the rate of the volume V of…

A: The volume of the right circular cylinder is given as: V=πr2h where 'r' is the radius of the cone…

Q: A spherical snowball melts at a rate of 2 cubic centimeters per hour. How fast is the radius…

A: We know that the volume of a spherical snowball is v = 43πr3 where v is the volume and r is the…

Q: The volume of a cube decreases at a rate of 0.75 ft3/min. What is the rate of change of the side…

A: Consider a cube with side 'a' The rate at which the volume of cube is decreasing is 0.75 cubic feet…

Q: Water is running out of a conical funnel at the rate of 1 in3/sec. If the radius of the base of the…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 4 cm2/min, find the rate at…

A: To find the rate at which the diameter decreases when the diameter is 12 cm and surface area…

Q: The radius of semicircle is increasing at the rate of 0.8 cm/s, calculate the rate of change in the…

A:

Q: a kite at a height of 60 ft is moving horizontally at a rate of 5 ft/sec away from the boy who flies…

A: Let boy is at the point A, and when 100 ft cord is released the kite is at the point C, which is…

Q: A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At which rate is the angle…

A: Given,  Consider the height of the lite from the ground is 100 ft. The speed is dxdt=8 ft/s. To find…

Q: A spherical balloon is being deflated at the rate of 10 cm/s. What is the rate of change for the…

A:

Q: The side of a square is increasing at the rate of 0.2 cm/sec . Find the rate of increase of the…

A: we know that the perimeter of the square is with side x is                        P=4x…

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

A:

Q: A conical cup is 4 cm across and 6 cm deep. Water leaks out of the bottom at the rate of 2 cm3 /sec.…

A:

Q: Rain is falling into a cylindrical barrel at the rate of 20 cm3/min. If the radius of the base is 18…

A: