The radius of a spherical balloon is measured to be 9 inches, with a possible error of 0.03 inch. Use differentials to approximate the maximum possible error in calculating the surface area of the sphere. Round your answer to two decimal places, if necessary.

Q: A circular plate is measured to have a diameter of 3.5 feet if the measurement could be off by as…

A: Given, The diameter of the circular plate,d=3.5feet The radius of the circular…

Q: A conical tank has height 3 m and radius 2 m at the base. Water flows in at a rate of 2 m^3/min.…

A: Given Height of canonical tank=3 m and Radius of canonical tank =2 m and dvdt=2 m3/min.     .....1

Q: a car braked with a constant deceleration of 20ft/s^2, producing skid marks measuring 350 ft before…

A: Measuring distances in feet and time (starting with the brakes being applied ) in seconds we have…

Q: The measurement of the side of the cube is 6 cm long. If this length has an error of 1/12 cm. Find…

A: Topic = Derivative

Q: The measurement of the edge of a cube is found to be 15 inches, with a possible error of 0.03 inch.…

A: Let ‘x’ be the edge of cube. Then

Q: he measurements of the base and altitude of a triangle are found to be 38 and 42 centimeters,…

A: The solution is :

Q: A carton of mass 10 kg is at rest on a rough plane inclined at an angle of 25° to the horizontal.…

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Q: You are given the task of building a spherical water tower with an inner diameter of 27.6 m and…

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Q: The radius of a spherical balloon is measured as 8 inches, with a possible error of 0.02 inch. (a)…

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Q: .A ball 6 inches in diameter is to be covered by a rubber material which is in-thick. Using…

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Q: The width and length of a rectangle are measured to be 3 m and 5 m, respectively. These come with an…

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Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

A: Given : θ = 26.75°

Q: 3. The edge of a cube is measured to be 6 inches with a possible error of ±0.1 inch. Estimate the…

A: The error in measuring the edge of the cube is 0.1 inches. to find the error in the surface area and…

Q: The radius of a circular disk is measured and found to be 20cm, with a max error in measurement of…

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Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 17°,…

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Q: You measure the angle from the ground to the top of the building from a point 70 feet away from the…

A: Given: Base, x=70 ft Let height of the building = h A rough sketch of the given problem is as…

Q: A circle has a radius of 5 cm jf the radius is increased by 0.l mm., what is the estimated increase…

A:

Q: The measurements of an edge of a cube is found to be 15cm with a possible error of 0.01 cm. Use the…

A: We have a cube whose edge is 15 cm. The error in calculating the edge is 0.01 cm Now, this error can…

Q: One side of a right triangle is known to be 12 cm long and the opposite angle is measured as 30°,…

A: Part (a):To estimate the error in the length of hypotenuse.

Q: 3. Water is flowing into a vertical cylindrical tank at the rate of 24 cubic ft. /min. if the radius…

A:

Q: The base radius r and height h of a right circular cone is measured as 5 inches and 10 inches,…

A: The volume of a right circular cone is given as, V=13πr2h The volume of the cone is a function of…

Q: A right circular cone has a base radius of 6 feet and slant height of 10 feet. If the approximate…

A:

Q: The radius of a circular disk is given as 24 cm with a maxi -mum error in measurement of 0.2 cm.(a)…

A: The radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm. Let…

Q: 3. Water is flowing into a vertical cylindrical tank at the rate of 24 cubic ft. /min. if the radius…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: A hollow cylinder has a radius R of the outer surface, radius r of the inner surface and height h.…

A: Given, a hollow cylinder has a radius (R) of the outer surface, radius(r) of the inner surface and…

Q: The measurements of the base and altitude of a triangle are found to be 20 and 60 centimeters,…

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Q: The base of the Great Pyramid at Giza is a square that is 20 m on each side. (a) As illustrated in…

A: Answer is mentioned below

Q: The radius of a sphere is given as 27 cm with a maximum error in measurement of .05 cm. Use…

A: From the given data:Radius of the sphere r=25cmMaximum error in radius of the sphere Δrr=0.05…

Q: 2. Assume Barry Bonds's head is a perfect sphere. If Dr. Beeresgood measures Barry's head's radius…

A: Given: r=5.8 in∆r=±0.021 in

Q: The thickness of the shell is a = 0.9 centimeter. Use differentials to approximate the volume of the…

A: To approximate the volume of the shell using differentials. Given, thickness=0.9cm radius=100cm

Q: The base of the Great Pyramid at Giza is a square that is 230 m on each side. (a) As illustrated in…

A:

Q: V9.22

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Q: The inside radius of a pipe is 4.50 cm. By using differentials, find the approximate volume of metal…

A: According the problem, we have

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: 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: The outside diameter of a thin spherical shell is 12 feet. If the shell is 0.3 inch thick, use…

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Q: The altitude of a certain circular cone is the same as the radius of the base, and is measured as 5…

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Q: The measurement of the radius of the end of a log is found to be 28 inches, with a possible error of…

A: Solution:- It is given that the radius of the end of a log=28 inches. ⇒r=28 inches possible…

Q: 6. The radius of a sphere is measured to be 7 cm, with a possible error of + (1/10) cm. Estimate the…

A: Volume of sphere   V=3π​r3/4 Percentage error in volume    ΔV​×100/V=3×Δr​×100/r =3*1*100/10*7= 4.3…

Q: The measurements of the base and altitude of a triangle are found to be 38 and 56 centimeters,…

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Q: The measurement of the side of a square floor tile is 10 inches, with a possible error of 1/32 inch.…

A:

Q: One side of a right triangle is known to be 9 cm long and the opposite angle is measured as 30°,…

A: Part (a) Side of the triangle is 15 cm, and opposite angle 30 degree with possible error of ± 1…

Q: Use differentials to estimate the maximum error in the volume of a rectangular box with square base…

A: Here we find the error in volume by using differential.

Q: 4. Water is draining from a cylindrical tank at 2.52 L/sec. Assume that the water tank has a…

A: Given: Water is draining at a rate of  2.52L/sec=2520 cm3/sec The water tank has a diameter of 50…

Q: The skid marks made by an automobile indicate that its brakes were fully applied for a distance of…

A: Given - The skid marks made by an automobile indicated that its break were fully applied for…

Q: 13. The measurement of the edge of a cube is found to be 15 inches, with a possible error of 0.03…

A:

Q: A spherical balloon is expanding at a rate of 60n in.3 How fast is the surface area of the balloon…

A: Use formula of surface area of shpare and take derivative of that than put given values.

Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30°,…

A: Given, a One side of right triangle = 20c.m longand the opposite angle=30°=xpossible error=±1°Let…

Q: a machinist is required to manufacture a square metal plate with the side length of 5cm.  if the…

A: The length of the metal plate is x=5cm. The machinist is allowed an error of 0.3 cm. The area of the…

Q: Suppose a snowball remains spherical while it melts, with the radius r shrinking at 3 inch(es) per…

A: Given: The radius of the spherical snowball is shrinking 3 inches in a hour.To find the numerical…