The radius of a sphere, initially zero, increases at the rate of 6ft per sec. Find how fast the volume is increasing after 1 4 sec

Q: The edges of a cube increase at a rate of 2cm/s. How fast is the volume changing when the length of…

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Q: The side of a cube increases at the rate of 11 m/sec. Find the rate at which the volume of the cube…

A: givenside of cube(a)=5mdadt=11m/secVolume of cube (v)=a3differentiating with respect to…

Q: The volume V of a cube with sides of length x in. is changing with respect to time. At a certain…

A: Given The volume V of a cube with sides of length x inch Side of the cube is 6inch that is x=6 inch…

Q: 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: 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: Sugar is poured into a conical tank at the rate of 15cm3/sec whose bottom radius is always quarter…

A: The volume of a cone is given by the formula V=13πr2h. Where, V-volume, r-radius and h is the height…

Q: A spherical balloon is being filled with air at a constant rate of 3 cm3/s. How fast is the radius…

A: Let,Volume of sphere = VRadius of sphere = rRate at which the volume of sphere is increasing = dVdt…

Q: A ladder 20 ft. long leans against a vertical wall. If the top slides downward at the rate of 2…

A: topic - application of derivatives

Q: The radius of a sphere is increasing at a rate of 3 mm/s. How fast is the volume increasing when the…

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Q: The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing when the…

A: Given that the diameter= 100 mm So the radius is=r=1002=50 mm Given that the radius of a sphere is…

Q: A cylindrical tank with radius 5 m is being filled with water at a rate of 3 m°, Imin: How fast 1.…

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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: Two concentric circles are expanding, the outer radius at the rate of 5 ft/sec and the inner one at…

A: Let A1 and A2 be the areas of the inner and outer circles at any instant and 'A' be the area between…

Q: Water is poured into a conical tank 6 m across the top and 8 m deep at the rate of 10 m3min. How…

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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: The radius of a sphere is increasing at a rate of 4mm/s. How fast is the volume increasing when the…

A: The rate of change of the radius of the sphere, drdt = 4 mm/s To evaluate : The rate at which the…

Q: The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in…

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Q: A spherical snow ball is being made so that its volume is increasing at the rate of 8 ft /min. What…

A: given: dVdt=8 ft3 /min We have to find drdtwhen diameter of snowball is 4 ft i.e, radius= 2ft we…

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: The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the…

A: Volume of sphere= =43πR3 where R is the Radius of the sphere.

Q: . The volume of a cube is increasing at a rate of 10 cm³/min. How fast is the surface area…

A: Given : Volume a cube is increasing at a rate of 10 cm³/min.

Q: side

A: Please refer to the image below

Q: The volume V of a cube with sides of length x in. is changing with respect to time. At a certain…

A: Given that sides are increasing at the rate of 0.4 in./secSo, dx/dt= 0.4

Q: The volume V of a cube with sides of length x in. is changing with respect to time. At a certain…

A: Solved below

Q: The radius of a sphere is increasing at a rate of 5 mm/s. (a) How fast is the volume increasing when…

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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: A cylindrical tank with a radius of 5 m is being filled with water at a rate of 3m^3/min. How fast…

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Q: An edge of a variable cube is increasing at the rate of 10cm/sec.How fast the volume of the cube is…

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Q: If the radius of a sphere is increasing at a constant rate of 3 cm/sec, then the volume is…

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Q: A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant…

A: Given: A stone dropped into a still pond sends out a circular ripple whose radius increases at a…

Q: A spherical balloon is inflated so that its radius (r) increases at a rate of 1/3cm/sec. How fast is…

A: Vloume(V)=43πr3Differentiate w.r.t tdVdt=43π.3r2.drdt

Q: A spherical snowball is made so that its volume is increasing at a rate of 8 cubic feet oer minute.…

A: I set these up this way. what do we know?  dVdt= 8 ft 3/min What do we want?  drdt = ?   when d = 4…

Q: Air is pumped into a spherical balloon so that its volume increases at a rate of 100 cm /s. How fast…

A: d[r^n]/dr = n r^(n-1)

Q: A spherical drop of liquid evaporates at a rate proportional to tis surface area. If a given drop…

A: Given: The drop evaporates to 18 of its volume in 5 minutes

Q: A spherical snowball is melting in such a way that its surface area decreases at the rate of 1…

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Q: A cube is expanding in such a way that the length of its diagonal is increasing at a rate of 5…

A: Let y be the diagonal, x be the length of an edge and V be the volume of the cube at any time t.…

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

A: It is given that, the volume of a cube is increasing at the rate of 6 cm3/min.   The objective is to…

Q: The radius of a sphere, initially zero, increases at the rate of 6 ft per second. How fast the…

A: Given ,The radius of a sphere , initially zero , increases at the rate of 6 per second.The volume is…

Q: If the radius of a sphere increases at a rate of 0.5 m/sec, then the rate at which the volume of the…

A: Let the radius of the sphere be r. Then the volume of the sphere is: V=43πr3…

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: A spherical balloon is being filled with air at the constant rate of 2 cm³ How fast is the radius…

A: Given that The spherical balloon is being filled with air at constant rate of 2cm3/sec. Since the…

Q: The volume of the cube is increasing at the rate of 8 cm3 /sec.how fast is the surface area…

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

A: Given , Bacterial cell is in spherical shape.Let radius be 'r' μm . ∴ Volume of cell, v v = 43π…

Q: The volume of a cube is increasing at the rate of 9 cm3 /  sec. How fast is the surface area…

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Q: The radius of a sphere, initially zero, increases at the rate of 4 feet per second. Find how fast…

A: Solution :Given  the adius of a sphere, initially zero, increases at the rate of 4 feet per…

Q: A snowball is being made so that its volume is increasing at the rate of 8 ft3/min. Find the rate at…

A: The geometrical figure of a snowball is a sphere. The volume of a sphere of radius r is V=4/3×πr3.…