A right triangle has legs of length h and r and a hypotenuse of length 6. It is revolved about the leg of length h to sweep out a right circular cone. What values of h and r will maximize the volume of the cone?

Q: An open top box is to have a square base and and a volume of 13500 centimeter cube. Find the…

A: in a cube each face is square volume of cube =(side)3

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Q: An open box with a square base is to have a volume of 12ft^3. find the box dimensions that minimize…

A: The volume of a rectangular prism(cuboid) = l×b×h Let y = measurement of each side of the base, h =…

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Q: An open-top rectangular box is being constructed to hold a volume of 150 in?. The base of the box is…

A:

Q: A box with a square base and open top must have a volume of 32m3. Find the dimensions of the boxthat…

A: Given,  V=32 m3                                      ..........................(1) The amount of…

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Q: The lengths of the legs of a right triangle are 4 cm and 6 cm. If the triangle is rotated about one…

A: *to find :  greatest volume of cone. *concept : for getting max volume we need to revolve triangle…

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Q: An open-top rectangular box is being constructed to hold a volume of 400 in³. The base of the box is…

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Q: A rectangular building with a square front is to be constructed of materials that costs 18 dollars…

A: Solution of question is written in below steps.

Q: find the maximum valume of a cone given that the sum of the radius and height of the cone is 15 cm.

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Q: b. A container in the shape of a right circular cylinder with no top has a surface area of 15 ft?.…

A: We have to find the height and base radius for which the volume of the cylinder will be maximized.…

Q: A box (with no top) is to be constructed from a piece of cardboard with sides of length A and B by…

A:

Q: A box (with no top) is to be constructed from a piece of cardboard of sides A and B by cutting out…

A:

Q: A box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the…

A: To find the dimensions that minimize area

Q: An open-top rectangular box is being constructed to hold a volume of 350 in. The base of the box is…

A: First derivative of a function when equated to 0 gives us the critical points of the function where…

Q: Find the maximum volume of a cylindrical soda can such that the sum of its height and its…

A: we have to find the maximum volume of a cylindrical soda can such that the sum of its height and its…

Q: An open-top rectangular box is being constructed to hold a volume of 300 in³. The base of the box is…

A: Consider a  rectangular box of dimension x, y and z as shown in the figure.

Q: An open-top rectangular box is being constructed to hold a volume of 200 in3. The base of the box is…

A: Let the length is x, y is the breadth and z is the height of the box. Then, the base area is xy and…

Q: A box with a square base and open top must have a volume of4000 cm^3. Find the dimensions of the box…

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Q: a. A rectangular pen is built with one side against a bam. If 1100 m of fencing are used for the…

A: x=width  y=length  perimeter is given by p=2x+y here we have p=1100 1100=2x+y y=1100-2x . the area…

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: How tall should the file be to maximize the volume that it can hold?

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Q: A box with an open top is to be constructed from a square piece of cardboard with dimensions…

A:

Q: A rectangular box has a square base. If the sum of the height and the perimeter of the square base…

A: Explanation of the answer is as follows

Q: A one compartment vertical file is to be constructed by bending the long side of an 8 in. by 14 in.…

A:

Q: The pencil holder is to have a base that has the same sides and a surface area of 100 cm. What…

A: The box will be open from one end. The surface area of the box will contain the base and the 4…

Q: An open box is to be made from a square piece of cardboard measuring 15 inches on a side by cutting…

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Q: Show that (a) the total surface of the cube is twice the square of its diagonal, fo) the volume of…

A: Given- A cube with side s. To show- That Show that (a) the total surface of the cube is twice the…

Q: If a closed tin can of volume 16? in3 is to be in the form of a right-circular cylinder, find the…

A: Consider the provided question, In your question given, If a closed tin can of volume 16? in3 to be…

Q: In the quest for the perfect donut, you decide that to make it, you're going to rotate the graph of…

A: The graph is drawn as :

Q: A box with a square base and open top must have a volume of 4,000 cm³. Find the dimensions of the…

A:

Q: A box with an open top is to be constructed out of a rectangular piece of cardboard with dimensions…

A: Here, the volume of the box is given by: V=lbh Here, for the given box, l=9-2x, w=10-2x,h=x. So,…

Q: A trough with a rectangular base and rectangular sides has vertical trapezoidal ends and is 200 cm…

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Q: A Normal window is in the shape of a rectangle surmounted by a semi-circle. What is the ratio of the…

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Q: A metallic sheet is of rectangular shape with dimensions 1m x 2m. From each of its corners, a square…

A: Given height = 8 cm So, given that each one of its corners a square of side 8 cm is cut off  now,…

Q: A box with an open top is to be constructed from a square piece of cardboard with dimensions…

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Q: The volume of a right circular cone is 36 t. If its altitude is 3, find its radius.

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Q: A one compartment vertical file is to be constructed by bending the long side of an 8 in. by 12 in.…

A: The plastic sheet has dimension 8 in. by 12 in. Let x be the height of the compartment file which is…

Q: A box with a square base and open top must have a volume of 32,000cm3 . Find the dimensions of the…

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Q: A rectangular box with no top is to be constructed having a 125 cubic inches. What width r, in 2…

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Q: | We have 48 m? of material to build an open box with a square base. nine the dimensions of the box…

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Q: A box with a square base and open top must have a volume of 186624 cm. We wish to find the…

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Q: The sphere below on the left has a radius r = 3 cm. If the sphere is enlarged by a factor of 4, how…

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Q: The sum of the dimensions of a box with a sqaure base is 48 m. Find the maximum volume of the box.

A: Volume