The length of a rectangular prism is quadrupled, the width is doubled, and the height is cut in half. If V is the volume of the rectangular prism before the modification, express the volume after the modification in terms of V.

Q: If 2400 square centimeters of material is available to make a box with a square base and an open…

A: Given information: 2400 square centimeters of material is available to make a box Consider x is the…

Q: By cutting six small squares out of a rectangle, as in the picture below, one creates a pattern that…

A: The length of the initial piece of cardboard = 4 inches. The width of the initial piece of cardboard…

Q: If the volume of the square pyramid below is 384 and the sides (x) of the square base are each 14,…

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Q: A rectangular piece of cardboard, whose area is 198 square centimeters, is made into an open box by…

A: Let the length of the box is = x cm  width= y cm.  Given height= 2 cm  So the volume=2xy

Q: The area of the rectangular piece of cardboard shown below is 192 square inches. The cardboard is…

A: Given that:Area of square box, A=192 in2Dimension of corner square=3 inVolume of box, V=180 in3

Q: A rectangular prism has a length of 13 feet, a height of 2 feet, and a width of 4 feet. What is its…

A: the volume of a rectangular prism is given by V=l·w·h here we have length l=13 feet  width w=4 feet…

Q: If you have a cone whose height is 10 cm and a radius of 3cm, how will the volume change if the…

A: given,       If you have a cone whose height is 10 cm and a radius of 3cm.     and if the height…

Q: A rectangular piece of metal is 30 in longer than it is wide. squares with sides 6 in. long are cut…

A: Consider the provided question,Let width of the rectangular piece of metal = x in.Length = (x + 30)…

Q: A rectangular prism has a volume of 8x^3+14x^2+x-2 and a height of 2x+1. Which expression represents…

A: See attached file for a step by step explanation to find the required area of the base of the…

Q: A rectangular piece of cardboard, whose area is 320 square centimeters, is made into an open box by…

A:

Q: A snack food company has decided to package its new brand of crackers in a box shaped like a…

A: Given data is : Volume=10834 cubic inches=108.75 inch3 Widthw=714inch=7.25inch Depth d=114 inch=1.25…

Q: ) The length of the box is 9 inches more than its width. The height of the box is 1 inch less than…

A: Given: Length is 9 inches more than width. Height is 1 inch less than width. Volume = 72 inch3

Q: A photographer decides to reduce a picture she took in order to fit it into acertain frame. She…

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Q: 2. Each edge of a cube is decreased by 1 inch. If the volume of the smaller cube is 37 cubic inches…

A: Given, Each edge of a cube is decreased by 1 inch. If the volume of the smaller cube is 37 cubic…

Q: If 1600 square centimeters of material is available to make a box with a square base and an open…

A: find the explanation below

Q: Two spheres have surface areas of 36cm squared and 49 cm squared. If the volume of the smaller…

A: Surface area of smaller sphereA1 is 36 cm2. Surface area of larger sphereA2 is 49 cm2. Consider the…

Q: A company that manufactures round disks that are used for weightlifting will double the diameter of…

A: Mass of the disk = Volume * density

Q: Find the volume of the largest box with no top that can be made from a piece of cardboard 30 inches…

A: Given that a box with no top has to be made from a piece of square cardboard of side  30 inches by…

Q: If 1500 square centimeters of material is available to make a box with a square base and an open…

A: We can solve the given problem by using the second derivative test.

Q: If 1900 square centimeters of material is available to make a box with a square base and an open…

A:

Q: RECTANGULAR PIECE OF METAL IS 10 IN. LONGER THAN IT IS WIDE. SQUARES WITH SIDES 2 IN LONG ARE CUT…

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Q: If a cube has the volume of 125 Cm°, and its sides have increased so that its volume is now 3375cm.…

A:

Q: When the height of the metal in the mold is 11 centimeters , the volume of metal in the mold will be…

A: Consider:

Q: If 2100 square centimeters of material is available to make a box with a square base and an open…

A:

Q: A rectangular piece of metal is 15 in longer than it is wide squares with sides 3 in long are cut…

A:

Q: The length of a rectangular pool is to be four times its width, and a sidewalk of width 6 feet will…

A: Lets assume width of a rectangular pool = x So length of a rectangular pool = 4x

Q: A rectangular piece of cardboard, whose area is 143 square centimeters, is made into an open box by…

A:

Q: A box with no top is to be made by cutting a 2-inch square from each corner of the square sheet of…

A: Solution : From given square sheet of metal as shown in the question.  Given that , The sheet of…

Q: The volume of the water in a rectangular swimming pool is V = 4x + 28x? + 40x if the height is 4x…

A:

Q: If 2300 square centimeters of material is available to make a box with a square base and an open…

A: Finding the maximum volume by differentiating the volume function

Q: A snack food company has decided to package its new brand of crackers in a box shaped like a…

A: The volume of the box is 108 3/4 cubic inches. Volume=108 34 in3=108.75 in3Width=714 in=7.25…

Q: Find the dimensions of a rectangle with area 1000 square meters whose perimeter is as small as…

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Q: The volume of a cylinder can be expressed as V = rr²h, whereris the radius, and h is the height of…

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Q: The length of a rectangle is twice its width. If the perimeter of the rectangle is 60 in, find its…

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Q: Find the width for this rectangular prism if the length is 12 cm, the height is 5 cm, and the volume…

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Q: The top and bottom margins of a poster are a cm and the side margins are each b cm. If the area of…

A: First draw the figure accordingly and solve:

Q: A rectangular piece of cardboard, whose area is 168 square centimeters, is made into an open box by…

A: Consider a rectangle  piece of cardboard whose length is x centimeters, breadth y centimeters and…

Q: Mr. Trombley says that half a sphere stacked on top of a cone roughly models an ice Cream cone. Find…

A:

Q: The shape of a Norman window can be approxiamated by a rectangle with a semicircle on the top. What…

A:

Q: If 1100 square centimeters of material is available to make a box with a square base and an open…

A:

Q: a cube can be filled up to (2x +1)3  cm3   and contains 16x2 +16x + 4cm of sand. Draw the figure and…

A:

Q: The height of a cube furnitore piece is x+10 inches, If the volume of the cube is x+1000 CU. in. how…

A: Given that,Height of cube, h=(x+10) inchesVolume of cube,v=(x3+1000)cu.in=(x3+103)cu.in

Q: When a body is immersed in water in a right circular cylinder 60 cm. in diameter, the level of the…

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Q: The dimensions of a rectangular prism can be expressed as x + 1, x − 2, andx + 4. In terms of x,…

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Q: If the volume of the square pyramid below is 990 and the sides (x) of the square base are each 16,…

A:

Q: A rectangular piece of sheet metal has a length that is 10in. less than twice the width. A square…

A: we will assume the width of sheet as x and then solve the resulting equation in one variable. volume…

Q: Find the dimensions of a rectangle with area 1,000 m² whose perimeter is as small as possible. (If…

A: According to question,

Q: A box has a volume of 48 cubic inches. If all the dimensions of the box are cut in half, what is the…

A: According to the question:

Q: A pasta box has dimensions of 6 x 4 x 3 inches.  If each measurement is reduced by ½ inch, how much…

A:

Q: If 2200 square centimeters of material is available to make a box with a square base and an open…

A: