a wire measuring 12 ft long is cut into two pieces. once piece is to be bent into a square and the other into a circle. how should the wire be cut so that the combined area is as large as possible?

Q: A gutter with trapezoidal cross section is to be made from a long sheet of tin that is 18 inches…

A: Given that , Total length of the sheet = 18 inches find width across the top will give the greatest…

Q: The volume of a sphere is 2,240 yards ^3. What will be the new volume if the dimensions are…

A:

Q: A jar is filled with marbles that are 1 cm in diameter. If the jar is a rectangular prism that…

A:

Q: One cake is rectangular with a length of 14 ​inches, a width of 10 ​inches, and a height of 2…

A:

Q: the base of the prism is a rectangle whose length is 3 cm more than the width. of the altitude of…

A:

Q: An open-top box is to be made by cutting small congruent squares from the corners of a…

A: Let the length of the side of the square is x in So the height of the box= x in  Length = (12-2x) in…

Q: Two chicken coops are to be built adjacent to one another from 168 ft of fencing.

A:

Q: what has a greater volume, a cube with side length 20cm or a sphere with diameter of 20cm?

A: we have a=20 cm     FORMULA

Q: An open box with a volume of 128 cm³ can be made by cutting a square of the same size from each…

A:

Q: A 6 ft board is cut into two pieces, one twice as long as the other. How longare the pieces?

A: Let the length of one piece = x ft length of other piece = 2x ft

Q: The sides of a square are 4 cm long Calculate the length of a diagonal

A: To calculate the length of the diagonal if the side of the square is 4 cm.

Q: A farmer has a 200 ft by 40 ft rectangular field that he wants to reduce to 45% of its original…

A: Solve the following

Q: A pole 27 feet long is carried horizontally along a corridor 8 feet wide and into a second corridor…

A: The diagram will be

Q: A rectangular box with a volume of 720 ft is

A: The volume of the rectangular box is 720 ft3. From the provided diagram, the height of the box is y…

Q: A cube shaped box has a volume of 125 inches.  If the box is packed full of cubes with edge lengths…

A: Vbigger box = 125  cubic inchEdge length of small cube = 1 inchVolume of one small cube, Vsmall cube…

Q: A square plot of land has a building 60 ft long and 40 ft wide at one corner. The rest of the land…

A: The building will cover an area about 60×40=2400 sq ft. The parking lot covers an area about 12000…

Q: the area of a regular pentagon and a regular hexagon are equal to 12 sq.cm. what is the difference…

A:

Q: Suppose a Red Oak is 30 ft high with a tree trunk radius of 2.5 ft and a Birch tree is 50 ft high…

A:

Q: A wire 20 inches long will be cut into two parts, one to be bent to form a square and the other to…

A: We have to find side of Square and diameter of the circle

Q: A rectangular piece of metal is 5 in longer than it is wide. Squares with sides 1 in long are cut…

A: Given: Volume of box = 374

Q: A rectangular lot 60 ft. Iong and 30 ft. wide is to be surrounded by a fence with posts 6 ft apart.…

A:

Q: A farmer has a 40 ft by 50 ft rectangular field that he wants to reduce to 10% of its original size.…

A: Let's find.

Q: A jeweler has three small solid spheres made of gold, of radius 2 mm, 3 mm, and 4 mm. He decides to…

A: Let the radius of large sphere be x. The volume of the large sphere is 43πx3. Model the equation for…

Q: A hemispherical tank is filled with water and has a diameter of 22 feet. If water weighs 62.4 pounds…

A: the volume of a hemisphere is given by  V=23πr3 here diameter is 22 feet so the radius is r=11 feet…

Q: A ladder that is 5 feet long is resting against the top of a wall that is 4 feet high. How far away…

A:

Q: The perimeter of a trapezium is 52 cm and its each non - parallel side is equal to 10 cm with its…

A:

Q: A piece of cardboard 4 ft by 4 ft will be made into an open topped box by cutting squares out of…

A: Summary... Cut should be of size  2/3 ft

Q: here is a rectangular lot in the garden, with 8 ft in length and 6 ft in width. You plan to expand…

A:

Q: A 6 ft board is cut into two pieces, on twice as long as the other. How longare the pieces?

A: Let the length of first piece = x ft Length of secind piece = 2x ft

Q: a rectangular prism tank has a base with a length of 40 inches a width of 35 inches and a height of…

A:

Q: A right triangle has an area of 84 ft2 and a hypotenuse  25 ft long. What are the lengths of its…

A: A triangle is a polygon having three sides and three vertices. The sum of the interior angles of…

Q: What will it cost to cover a rectangular floor measuring 40 feet by 50 feet with square tiles that…

A:

Q: A rectangula plot of land is to be seeded with grass. If the plot is 16 m by 12 m and a 1kg bag of…

A:

Q: An open box, no more than 5 cm in height, is to be formed by cutting four identical squares from the…

A: The dimension of the metal sheet is 25 cm by 32 cm. Let x cm be the side length of the squares…

Q: The sides of a trapezoid are each 8 cm long. How long is the 4th side, when the area of the…

A:

Q: A rectangular lot which has an area 120sq.m will be divided into two portions such that the product…

A: Consider the rectangular is divided into two portions with areas x and y. So, x +y = 120…

Q: Find the edge of a cube whose volume is equal to that of a rectangular bar measuring 126 cm long, 4…

A:

Q: Two trim boards need to be used together to cover a 12-ft length along one wall. If Jim recalls that…

A: Given that two trim boards need to be used together to cover a 12-ft length along one wall. And one…

Q: he face of the right triangular

A: Given,

Q: ngular horse corral has one side measuring 27.7 ft., a second side measuring 45.6 ft., and a third…

A:

Q: A 60 foot ladder needs to reach a window that is 47 feet off the ground . How far away to the…

A: Ans (1) we have given a 60 foot ladder needs toreach a window that is 47 feet the groundAs 1 feet =…

Q: How many cubic feet of soil must be excavated to make a railroad embankment 200 ft long if a cross…

A: Solve by using mensuration formulas

Q: An office, 5 m long, 4 m wide and 2.5 m high, is to have its walls covered with plywood panels. The…

A:

Q: A square plot of land has a building 80 ft long and 20 ft wide at one corner. The rest of the land…

A: Let x be the side of the square land area.

Q: For a given box, the height measures 6 m. If the length of the rectangular base is 2 m greater than…

A: Given: length of the box=l=2+width=2+wwidth=w=?   and height=h=6Also…

Q: An artist is contracted to paint a mural on the rectangular side of a building. If the dimensions of…

A:

Q: A single-story shopping center is being designed to be 483 ft long by 90 ft deep.

A:

Q: A farmer has a 25 ft by 40 ft rectangular field that he wants to reduce to 10% of its original size.…

A:

Q: An artist is contracted to paint a mural on the rectangular side of a building. If the dimensions of…

A: The dimensions of the wall are 149 ft by 74 ft.