The surface area of a sphere is expanding at the rate of 6 cm²/sec, Wher What is the change in the radius when r = 2? dr 3 cm/s dt dr 3 cm/s 4 T7 dt dr dt 27 cm/s dr 1 am (s

Q: Use the area shown in the figure to find the value of each integral. a) S S(x) dx: у-аxis Area = 0.6…

A: The value of each integral given the area over the given integral  ∫abf(x) dxFrom x=a  to 0 the area…

Q: Assume that the radius r of a sphere is expanding at a rate of 30 cm/min. The volume of a sphere is…

A: For the given sphere: Rate of expansion of radius r=30 cm/min……1At t=0, r=10 cm……2Surface area, say…

Q: The electrical charge distribution on a circular plate of radius R meters is s(r, θ) = kr(1 - sin θ)…

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Q: 1. Water is flowing into a vertical cylindrical tank at the rate of 24 ft3/min. If the radius of the…

A: As per guidelines, we are supposed to solve only first two questions. Please repost other questions…

Q: Q3:Oil is draining from a conical filter with adimension(6 in in diameter ,6 in height) into a…

A: Rate of change

Q: dX If the side of a cube is expanding at the rate d = 2t cm/sec, and X(0) = 3 cm. What is the volume…

A: This question can be solved using the concept of differential equation.

Q: Air is being pumped into a spherical balloon so that its volumeincreases at a rate of 100 cu. cm /s…

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Q: A spherical balloon is being inflated. Find the rate (in ft2/ft) of increase of the surface area (S…

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Q: The volume of a cylinder is fixed at a value of V. Find how fast the radius of the cylinder changes…

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Q: A tank is shaped like an upside-down square pyramid, with base of 5 m by 5 m and a height of 14 m.…

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Q: A right trianglewith dimensions of X = 3 cm and y =4cm.if Cx) is increasing at arate of 2 cml sec…

A: We will find the rate of change in z

Q: A hemispherical dome has a diameter of 100 m. A searchlight was placed at a point A located at the…

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Q: The radius of a sphere decreases at a rate of 8 m/sec. Find the rate at which the surface area…

A: We will solve the following.

Q: A spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute. Find the…

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Q: Coffee is draining out of a conical filter at a rate of 2.25 in³/min. If the cone is 4 in all and…

A: The volume of cone is given by . The rate of coffee draining is 2.25 cubic inch per minute. This…

Q: What is the rate of change of the volume of a ball (V = (4/3)pai r3 ) with respect to the radius…

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Q: A cone with an altitude of 40 cm has its base radius changing at the rate of 2 mm/s. How fast is its…

A: The lateral surface area, S, of a cone is calculated using the formula: S=πrr2+h2, where r, h are…

Q: Consider a closed rectangular box with dimensions ft by y ft by z ft. If is increasing at the rate…

A: Given:    dxdt=4 ft/min    dydt=-6 ft/min     dzdt=3 ft/min To find dDdt when x=18 ft, y=10 ft,z=4…

Q: The radius of a sphere is decreasing at a rate of 1/4 cm/s. At what rate is the volume decreasing if…

A: Volume of the sphere , V=43πr3

Q: The volume of a sphere is expanding wherer = 2t. What is the rate of change in volume with respect…

A: "Since you have asked multiple question, we will solve the first question for you.If you want any…

Q: A balloon which maintains the shape of a sphere is being inflated. The rate of change of its volume…

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Q: Water is poured into the bucket below at a volume rate of 10 cm³/s. The surface area of the bucket's…

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Q: #Ś A spherical balloon is filled with helium at a rate of 200 cmsec.At the moment when the radius is…

A: we have to find the rate change of surface area of the spherical balloon

Q: The volume of a sphere is expanding where r= 2t + 1. What is the rate of change in volume with…

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Q: Sand is poured onto a surface at 11 cm³/sec, forming a con- ical pile whose base diameter is always…

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Q: The radius of a sphere decreases at a rate of 2 m/s. when the radius is 6 m, then the rate at which…

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Q: The volume of a right-circular cone of radius r and height h is represented by V = (1/3)r2h.…

A: Given that, The volume of a right circular cone of radius r and height h is represented by V=13πr2h…

Q: A triangular trough is 3.6 meters long, 1.2 meters 0.9 meter wide at the top as shown in the figure…

A: To evaluate the volume of the water, use the formula for the triangular trough, V=Ah, where A is the…

Q: The volume of a right circular cone is given by V(r,h)=πr^2h/3. Find the differential dV.

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Q: A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the…

A: Here, given that the volume is constant. So, dVdt=0⇒ddtπr2h=0⇒πh 2rdrdt+r2dhdt=0⇒h 2rdrdt+r2dhdt=0…

Q: The spherical balloon is being filled at a constant rate of 3cm/sec. How fast is the radius…

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Q: The volume of a metal in a hollow spherical is constant. If the inner radius is increasing at thr…

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Q: Assume that the radius ? of a sphere is expanding at a rate of 40 cm/min. The volume of a sphere is…

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Q: Air is being pumped into a spherical balloon so that its volume increases at a rate of 20cm³ /s. How…

A: We have given the  Rate of change in volume = 20cm3/sec  We have to find the change in surface area…

Q: A sphere is expanding with time. Assume that the volume of the sphere is y = r(t) = t + 2. What is…

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Q: An inverted conical tank is being filled with water at the rate of 2ft3 per minute. If the tank has…

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Q: hA balloon is being fi ned with helium at the rate Off 4 f+%A Fld the rate in 8quare teet per Minute…

A: The volume of a balloon with radius r will be V=43πr3 and surface area will be S =4πr2 Given: dVdt=…

Q: As above, a particle has velocity v(t) = 3t² – 2t – 1, measured in meters per second. Now compute…

A: We have to find

Q: A conical cup is 6 inches tall, and the top of the cup has a radius of 3 inches. Water is being…

A: Given, The volume of a cone of height h and radius r is given by, v=13πr2h Here we use the units,…

Q: Water is poured into the bucket below at a volume rate of 10 cm³/s. The surface area of the bucket's…

A: Here we have to use Fundamental  theorem of calculus Part 1 Let f be a continuous real-valued…

Q: The Volume of a Sphere is increasing at the rate of 8 m³; how fast is its Radius increasing when the…

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Q: How can you relate the rate of change for the surface area of a cube (dSA/dt) as compared with its…

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Q: The volume of a sphere is expanding where r = 2t. What is the rate of change in volume with respect…

A: First substitute the value of r=2t in volume ,and then differentiate it for finding the rate of…

Q: A sphere is expanding with time. Assume that the volume of the sphere is V = (4pi * r ^ 3)/3; r(t) =…

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Q: Find the rate of change of the volume (V) of a sphere with respect to its radius (r) when r = 4. 4π…

A: You must have idea about basics of derivatives. The rate of anything is basically the derivative…

Q: Q3: A right circular cone has the radius of the base and the height which at a given instant (to)…

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Q: 2. How can you relate the rate of change for the surface area of a cube (dSA/dt) as compared with…

A: we know that surface areaSA and volumeV of a cube, whose side is l given by SA=6l2…

Q: A spherical balloon is being inflated at a constant rate of 20 cubic inches per second. How fast is…

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Q: Water flows into a cylindrical tank through pipe 1 at the rate of 25 ft/s and leaves through pipes 2…

A: Water flow into a cylindrical tank through pipe 1 is 25 ft/sec rate.  And pipe 2 is 10 ft/sec. And…

Q: A spherical balloon is being inflated. Find the rate (in ft?/ft) of increase of the surface area (S…

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