) The volume of a right circular cone is πr^2h/3 where r is the radius of the base and h is the height of a cone. Use the disk method to derive this formula.

Q: 4. A container with square base, vertical sides, and open top is to be made from 1000 ft2 of…

A: Volume of box is x2 y where x is the base and y is height of the box.

Q: Find the height of the right circular cylinder of maximum volume that can be inscribed in a sphere…

A: Given, A sphere of radius 15 cm  We have to find the height of the right circular cylinder of…

Q: A right circular cylinder with an altitude of 40cm and base diameter of 30cm has a right circular…

A: Recall:  Lateral are of cone, AL=πrl We have, l=60cm, diameter=30 cm, radius, r=15 cm

Q: 3. Solve for the volume of a right octagonal pyramid where the perimeter of the regular octagonal…

A: Consider the given: Since the perimeter of the regular octagonal base is 0.1 meter. Let the side of…

Q: 3. Find the volume of the largest right-circular cylinder that can be inscribed in a right-circular…

A: As per bartleby guidelines, for more than one questions, first one needs to be solved. The diagram…

Q: Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of…

A:

Q: A pool in the shape of a right rectangular prism is 15 m long, 9m wide, and 2 high. What is the…

A:

Q: The sphere of diameter 24 cm is cut by two parallel planes, one passing 4 cm from the center and…

A: d = 24 cm one plane 4 cm from the center second plane 7 cm from the center

Q: A box is to be made of a piece of cardboard 9 in. square by cutting equal squares out of the cormers…

A:

Q: Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of…

A: Let h is the dimension  of the square which are being cut at each corner of the cardboard, so The…

Q: A hemispherical bowl of radius 5 cm is filled with water to within 3 cm of the top. Find the volume…

A:

Q: A right prism has square bases with edges that are three times as long as the lateral edges. The…

A: Given that a right prism has square bases with edges that are three times as long as the lateral…

Q: A vessel in the shape of a cone has a height of 48 cm and a base diameter of 16 cm. It holds water…

A:

Q: right triangle with base width of 6 and height of 3 have its right-angle corner at coordinate (6,…

A: Given query is to find the volume of the solid generated.

Q: Find the height of a right circular cylinder of maximum volume, which can be inscribe in a sphere od…

A:

Q: A cone is formed from a circular piece of material of radius 1 meter by removing a section of angle…

A:

Q: Find the dimensions and volume of the right circular cylinder of maximum volume inscribed in a…

A:

Q: A vessel in the shape of a cone has a height of 48 cm and a base diameter of 16 cm. It holds water…

A: Given,  Height of cone= 48 cm Base diameter = 16 cm Radius of cone = 8 cm  Depth of water = 18 cm…

Q: Determine the dimensions of the right circular cylinder of greatest volume that can be inscribed…

A: We have to find the dimensions of the right circular cylinder of greatest volume that can be…

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

A: The schematic representation is shown below. Since the box is open at the top, the volume of the…

Q: Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of…

A:

Q: A cylinder with length 1 m and radius 5 cm has a cone of the same radius and length of 10 cm…

A: We will find out the required value.

Q: With a rectangular piece of metal 150cm by 200cm, cut out squares from each corner in order to…

A: I use second derivative method to find dimensions of box where volume maximum

Q: Find the dimensions of the right circular cylinder of greatest volum that can be inscribed in a…

A: Given query is to find the dimensions of a right circular cylinder that can be fit inside a sphere…

Q: 2. A right cylinder is inscribed in a cone with height 3 cm and radius of 9 cm. Find the largest…

A: We have to find the largest volume.

Q: A box is to be constructed from a piece of zinc 20 inches square by cutting equal squares from each…

A:

Q: A large cube is formed from the material obtained by melting three smaller cubes of 3, 2 and 1 cm…

A:

Q: Find the height of a right circular cylinder of maximum volume, which can be inscribe in a sphere of…

A:

Q: From a solid cube of side 7 cm , a conical cavity of height 7 cm and radius 3 cm is hollowed out…

A:

Q: A square hole of side 2 cm is chiseled perpendicular to the side of a cylindrical post of radius 2…

A:

Q: A right circular cylinder and a right circular cone with the same circular base and same length of…

A: Given that A right circular cylinder and a right circular cone with the same circular base and same…

Q: 9. A right pyramid has a height of 45 meters and a square base with sides 60 meters long. Determine…

A:

Q: 7. Find the dimensions of the right circular cylinder of greatest volume that can be inscribed in a…

A: Given

Q: A closed cylindrical tank is made of a metal sheet having an area of 43.82 square meter. If the…

A:

Q: Solve for the volume of a right octagonal pyramid where the perimeter of the regular octagonal base…

A: volume of a right octagonal pyramid

Q: determine the dimensions of a rectangular tank open at top having the volume of 108 cm^3 and…

A: Finding the dimensions of the box using the given conditions

Q: 8) A right circular cylinder must have a volume of 100 m3. Find the dimensions that should be used…

A: Let, radius= r height = h

Q: A cone is formed from a circular piece of material of radius 1 meter by removing a section of angle…

A: To determine the largest possible volume for the cone, if a cone is formed from a circular piece of…

Q: A box with an open top is to be constructed from a square piece of cardboard, 3 m wide, by cutting a…

A: 1) Given:

Q: 2. Find the height of a circular cylinder of max. volume that can be cut from a spherical wood of…

A:

Q: . A box with a square base and open top must have a volumeof 32,000 cm cu .  . Find the dimensions…

A: To Determine: Find the dimensions of the box that minimize the amount of material used Given: A box…

Q: A 60 m long pipe of metal is cut into two pieces. One piece is used to form a square and the other…

A: Perimeter of square =4a 4a=x Perimeter of triangle =3b 3b=60-x b=(60-x)/3

Q: Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of…

A:

Q: Determine the dimensions (radius and height) of the largest right circular cylinder. volume that can…

A: Solution:-

Q: A box is to be constructed from a piece of zinc 20 inches square by cutting equal squares from each…

A: Given- A box is to be constructed from a piece of zinc 20 inches square by cutting equal squares…

Q: Find the dimensions of a right-circular cylinder of greatest volume that can be inscribed in a…

A: Given that: A sphere of radius 10 in.

Q: An inverted square pyramid has a height equal to 8 m and a top edge equal to 3 m. Initially, it…

A:

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.