34) The volume of a rectangular box with a square base remains constant at 1200 cm3 as the area of the base increases at a rate of 11 cm2/sec. Find the rate at which the height of the box is decreasing when each side of the base is 15 cm long. (Do not round your answer.)

Q: 2. Sand is being dropped at the rate of 10ft.3/min into a conical pile. If the height of the pile is…

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Q: 4. A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate…

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Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 5 cm/min.…

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Q: The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is…

A: Given that, drdt=1.1 in/s and dhdt=-2.7 in/s. Also, it is given that r=102 in. and h=162 in. It is…

Q: 11. If a snowball melts so that its surface area decreases at a rate of 1 cm/min, find the rate at…

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Q: The ice cream in a sugar cone (conically shaped) has all melted and is dripping out a hole in the…

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Q: 7) A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15…

A: Given: A spherical balloon is to deflated so that its radius decreases at a constant rate of 15…

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A: It is given that the cone has altitude 16 m and radius 4 m. That is, hcone=16,rcone=4. Let r and h…

Q: A conical vessel 12 cm deep and with a radius of 6 cm at the top, is being filled with water. If the…

A: A conical vessel 12 cm deep and with a radius of 6 cm at the top. That is, the height of the cone is…

Q: A cube has sides that are increasing at a rate of 10 cm/s. At what rate is the volume increasing…

A: Valur=?

Q: 3 The volume of a cube is increasing at the rate of 8 cm³/sec.How fast is the surface are increasing…

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Q: 7. A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base…

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Q: Suppose the edges of a cube are increasing at a constant rate of 11 m/hr. Then, the volume of the…

A: Let the side of the cube = x Edges of the cube increasing rate dx/dt = 11 m/hr

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Q: The radius of the base of a right circular cone is decreasing at the rate of 4 cm/min, and the…

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Q: Water is being poured at the rate of 27 m³/min. into an inverted conical tank that is 12-meter deep…

A: Given that a canonical tank that had radius is 6meter and height is 12 meter and dh/dt= 1/6…

Q: 2. A water tank is in the form of an inverted right circular cone h feet deep and d feet wide across…

A: At any time t, let the height of the water be h ft and the radius of the cone formed by the volume…

Q: Water is being released from a conical reservoir (vertex down) 20 ft in radius and 40 ft deep at a…

A: Use similar triangle to shoe that  r/20 = h/40 where r and h are the radius and height of water in…

Q: a) Water is flowing into a leaky cistern at the rate of 31.4 cu ft./min. The cistern is a right…

A: Given that  The water is flowing into a leaky cistern at the rate of 31.4 cu ft./min ⇒dVdt=31.4…

Q: A trough whose cross section is an equilateral triangle is 6 m long and 2 m wide across the top. If…

A: Solve by diagram and using formulas of equilateral triangle

Q: 9) A spherical snowball is melting in such a way that its volume is decreasing at a rate of 3cm /…

A: Let, r=radius  V=volume Given that dV/dt= 3 , we have to find dr/dt=? at r=12 cm Volume and radius…

Q: A balloon, in the shape of a right circular cylinder, is being inflated in such a way that the…

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Q: The radius of a right circular cone is increasing at a rate of 1.2 in/s while its height is…

A: To calculate the required rate of change using partial derivatives

Q: The volume of a cube increases at a constant rate of 135 ft°/ sec. The rate at which the side of the…

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Q: The original 24 m edge length x of a cube decreases at the rate of 2 m/min. a. When x = 1 m, at what…

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Q: A spherical balloon is inflated at a rate of 10 cm3>min. At what rate is the diameter of the…

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Q: 2. Suppose that the bottom of a conical shaped tank of water has been ruptured. At the instant when…

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Q: The sides of a square increase in length at a rate of 3 m/sec. a. At what rate is the area of the…

A: let the side of the square is a meter, and the area is A given that da/dt=3m/sec a. a=15m area of…

Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15 cm/min.…

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Q: 17. If the radius of a sphere is increasing at the constant rate of 3 inches per second, how fast is…

A: Given: The radius of the sphere is increasing at the constant rate of 3 inches per second. To find:…

Q: 2. A cylindrical plastic container with a radius of 15 cm is being filled with orange juice at a…

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Q: A cone-shaped tank of water is leaking water at a constant rate of 2 m3/hour. If the base radius of…

A: Given that

Q: 3. The volume of a cube is increasing at the rate of 6 cm³/min. How fast is the surface increasing…

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Q: The volume of a cube is increasing at the rate of 1200 cm3/min at the instant its edges are 20 cm…

A: Let the length of the sides of the cube = xAnd the volume of the cube = V = x^3

Q: The two equal sides of an isosceles triangle with fixed base b are b are decreasing at the rate of 3…

A: Solution :-

Q: The radius of a right circular cone is increasing at a rate of 5 in/s while its height is decreasing…

A: Let,  r - radius of the right circular cone h-Height of the right circular cone  V- Volume of the…

Q: 11. At what rate is the volume of the cube changing if the edge is 8 cm and is changing at 4 cm/s?

A: As we know that; The expression for the volume of the cube with the edge length ''a'' is: v=a3…

Q: The volume of a cube is increasing at the rate of 1200 cm³ / min at the instant its edges are 20 cm…

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Q: 3. The area of a circular inkblot starts from zero and grows at a constant rate of 4n cm/minute.…

A: Use the derivative and formula for area of circle.

Q: An inverted conical tank 10 m high and 3 m radius at the top fills with water at a constant rate. At…

A: Given: An inverted conical tank 10 m high and 3 m radius at the top fills with water at a constant…

Q: 2) A kite is flying at a fixed height of 30 ft. If 50 feet of string is out already from the spool,…

A: Given- A kite is flying at a height of 30 feet, if 50 feet of string is out already from the spool…

Q: The radius of a right circulare cylinder is increasing at the rate of 3 in/sec, while the height is…

A: To determine the change of rate of the volume of cylinder.

Q: A bacterial cell is spherical in shape. If the radius of the cell is increasing at the rate of 0.01…

A: Volume of sphere: V = 43πr3, where r is radius of sphere. Surface area of sphere: S = 4πr2, where r…

Q: Suppose that a spherical balloon is being inflated and the radius of the balloon is increasing at a…

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Q: A spherical balloon has a radius r that is increasing at a rate of 3 emfs. At what rate is the…

A: Given: drdt=3πcm/s   To find: dvdt when r=10

Q: 7, If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at…

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Q: A horizontal trough is 16m long, and its ends are isosceles trapezoids with an altitude of 4m, a…

A: The derivative is also called the rate of change of a quantity with respect to time. The volume of a…

Q: All the edges of a cube are expanding at a rate of 1/6 cm/sec. Determine the rate of change of the…

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