5. Assume an American football has an ellipsoid shape and has a length of 27 cm and a height of 16 cm. The ball is hollow and filled with air. If it is to be sliced in half at the middle, running through its pointed ends, determine by integration the length of the cut.

Q: The line y = 2x and the parabola y = 16x intersect at x= 4. Find by a double integral, the area…

A:

Q: What are the dimensions of a closed rectangular box that has a square cross section, a capacity of…

A: x= 5.07 in y= 5.07 in

Q: 9 A copper sheet with 16 cm by 16 cm dimension has to be made as a square box with no top cover.…

A: Dimension of the copper sheet = 16 by 16 cm;                    Square corners…

Q: 14. Find the dimensions of a right cone with surface area S=4 n that has the largest volume?

A:

Q: The diameter and height of a paraboloid are 1 m and 2 m respectively. Determine its dimensions when…

A: Given, Diameterd=1 mHeighth=2 m The formula for finding the volume of the paraboloid is, V=π2hr2

Q: 5. Design a 4m³ open-top box shaped like a circular cylinder as shown in Figure. What dimensions…

A:

Q: 6. A bax with a square base is to have an open top. If the lateral surface of the bax is 100 cm",…

A:

Q: 7. A manufacture want to design an open box having a square base and a volume of 256 cm³. What…

A: Given problem is :

Q: A manufacturer is making cylindrical cans that hold 200 cm3. The dimensions of the can are not…

A:

Q: 9. A cylindrical tank of height 10 m and radius 3 m is full of water. How much work is required to…

A:

Q: 5. Suppose that a water tank is shaped like a right circular cone with the tip at the bottom, and…

A:

Q: As a hardworking student, plagued by too much homework, you spend all night doing math homework. By…

A: Region bounded by the curves

Q: A closed-top cylindrical can is to have a volume of 250 in3. a. What dimensions (radius and height)…

A: Given that volume is 250 in3.

Q: In constructing an open rectangular box from 75 ft² of material, what dimensions will result in a…

A:

Q: 2. A right triangle with hypotenuse of 5V3 cm. is revolved about one of its legs to generate a cone.…

A: Given,          Let r, h, and V be the radius, height, and volume, respectively

Q: Show that it is not possible to design a cylindrical can (with top and bottom) of volume 900 cubic…

A:

Q: 4. A right cylinder has a surface area of 28T cm² and a height of 5 cm. Solve for the radius/Show…

A: It is given that the surface area of a cylinder is 28π cm2 and its height is 5 cm.

Q: 11) A cone with radius 6cm and height 12cm is filled to capacity with liquid. Find the minimum…

A: To hold the same amount of liquid, the cylinder and cone should have same volume. Here the radius…

Q: Suppose that for the tank in Exercise 23 the pump breaks down after 4.7 X 10° J of work has been…

A:

Q: Suppose that a semicircular wire has the equation y= V25- x and that its mass density is 8 = b- y.…

A:

Q: Find the surface area of the portion of the half ball with radius a which cuts off by the cylinder…

A: The equation of a ball with radius a is x2+y2+z2=a2. The surface area of the function z=fx,y over…

Q: If the curve y = 4x², 2 ≤ x ≤ 5, is rotated about the x-axis, what is the integral that represents…

A:

Q: The base of a solid is the unit circle x^2+y^2=1 , and its cross sections perpendicular to the…

A:

Q: 1. A closed cylinder of volume 600 cm³ is made using a metal sheet. Find the radius that will…

A: The formula to calculate the volume of the cylinder is V=πr2h. And the volume is given as 600 cm3.…

Q: 4. A vertical right circular cylindrical tank measures 24 ft high and is 8 ft in diameter. It is…

A: Given:The height of the right circular cylindrical tank is 24 ft and diameter is 8 ft. It is full of…

Q: 14. A system of storm sewers in a coastal city is designed to capture water runoff during heavy…

A:

Q: 15 10 15 8 The cylindrical glass is full of water. Which is poured into the rectangular pan. Will…

A: Radius of cylindrical glass= 8/2=4

Q: Suppose div F = 0 in a region enclosed by two concentricspheres. What is the relationship between…

A: Apply the divergence theorem for the hollow region which is bounded by 2 surfaces. Consider D as the…

Q: 1. Find the dimensions of a rectangular box with a square base and no top that has a volume of 100…

A: Solve By minimizing surface area

Q: 5. Find the area of the surface of revolution generated by revolving .3 y = on interval [0,3] about…

A: Given: The function y=x33on interval 0,3, To find: The area of the surface of revolution generated…

Q: 14. The solid with a semicircular base of radius 5 whose cross sections perpendicular to the base…

A:

Q: A manufacturer of food-storage containers makes cylindrical can with a volume of 500 milliliters.…

A: A manufacturer of food-storage containers makes cylindrical can with a volume of 500 milliliters.

Q: A manufacturer needs to make a cylindrical can that will hold 1.5 liters of liquid. Determine the…

A:

Q: 8. A manufacturer needs to make a cylindrical can that will hold 1.5 liters of liquid. Determine the…

A:

Q: 4. Find the volume of the solid whose base is the region enclosed between the curve x = 1-y² and the…

A:

Q: (23) A right triangle with a hypotenuse of 6 inches is rotated about one of its legs to generate a…

A:

Q: What are the dimensions of a closed rectangular box that has a square cross section, a capacity of…

A: Here we want to find the dimensions of the given rectangular box having volume of 101 in³ it is…

Q: What radius (r) and height (h) of a cylindrical can holding 1L of oil that minimizes the  cost of…

A:

Q: A closed cylindrical tank of maximum volume is to be constructed. With only 381.7 m^2 of material,…

A:

Q: A manufacturer of food-storage containers makes cylindrical can with a volume of 500 milliliters.…

A: A manufacturer of food-storage containers makes cylindrical can with a volume of 500 milliliters. We…

Q: Assume we wish to to make a right cylindrical can with a bottom and no top, and with a capacity of…

A: Solve it

Q: A closed box with a square base is to be built and the volume fixed at 30 m3. Determine the minimum…

A: To determine the minimum cost of the box.

Q: 6. Show that when a hole of radius a is bored through the center of the sphere of radius b, the…

A: Given : The radius of the sphere is b. The radius of the hole is a. We have to show that the volume…

Q: A cylindrical tank, shown to the right, has height 8 m and radius 3 m. Suppose the water tank is…

A: Here, the density of water  ρ=1000 kg/m3&g=9.8 m/s2 Here, the radius of the cylindrical tank is…

Q: A storage reservoir with volume 32 m³ needs to be constructed (Figure Q5.c). The reservoir is shaped…

A: A function f(x) will have the maximum value at a point x when the derivative of the function is zero…

Q: Express

A:

Q: 17. Find the work done in pumping out water from the top of a cylindrical tank 3.00 ft in radius and…

A: To calculate how much work is done to empty the tank under the given conditions

Q: The base of a solid is the unit circle x2 + y2 = 1, and its cross sections perpendicular to the…

A: