A square with dimensions 12 cm, 2 cm, 9 cm and a cube have equal volumes. Calculate the edge of the cube.

Q: The total length of all the edges of a cube is 96 cm. Find the volume of the cube.

A: The total length of all the edges of a cube is 96 cm. To Find the volume of the cube.

Q: Of all rectangles of area 100, which has the smallest perimeter?

A: Given:  Area of rectangle =100     Let x and y  be the base and the height of the rectangle,…

Q: Among all rectangles that have perimeter of 20 ft, find the dimensions of the one with largest area?…

A: Let the dimensions for generalized rectangle be length l ft and width w ft. Find the perimeter and…

Q: A rectangular parallelipiped is of dimensions 5cm x 2cm x 5cm. How many such rectangular…

A: This question is based on LCM (least common multiple).

Q: The open-topped box can be created by cutting squares from the four corners of a 20cm by 30cm piece…

A:

Q: 3. Find the dimension of a rectangle with area 1000 m² whose perimeter is as small as possible.

A:

Q: Give the dimensions of a box with 5 sides that has a surface area of 300 cm? and holds the largest…

A: Let the dimension of the box is l×b×h, so the surface area of five-sided box is: S=2lb+2bh+lh Given,…

Q: If 900 square centimeters of material is available to make a box with a square base and an open top,…

A: Volume = A×A×H Where A is surface area and H is Hight

Q: Find the total area (surface area) of a regular dodecahedron (12 faces) if the area of each face is…

A: As we know, The dodecahedron is a regular polyhedron of 12 faces. If the mentioned faces are regular…

Q: Norman builds a rectangular pig pen with two parallel partitions using 150 meters of fencing…

A: let the length of Pig pen be "a"width be " b" Perimeter=150 metresPerimeter = 2(a+b)…

Q: 2. Find the dimensions of a rectangle with an area of 225 square cm, whose perimeter is as small as…

A:

Q: 3. Find the length of the diagonal of a cube whose volume is 27 cubic cm.

A:

Q: If 1400 square centimeters of material is available to make a box with a square base and an open…

A:

Q: Find the volume of a right triangular prism whose height is 4 and base is a right triangle with legs…

A: Find the area of base and then multiply the area with height.

Q: A rectangular solid whose dimensions are 4cm, 8cm, and 12cm is inscribed in a sphere. What is the…

A:

Q: Find the dimensions of a rectangle with an area of 225 cm2, whose perimeter is as small as possible.

A: Given that area of rectangle is 225 cm2.

Q: A block has a mass of 50 kg and a density of 8.91 gram per cubic cm. Find the largest area of a…

A: Mass of a block = 50 kg Density of a block =8.91g/cm3 Mentioned dimension are 10m, 12m, 12m.

Q: A page is to contain 54 sq cm. of printed material. If the margins are lcm at the top and bottom and…

A:

Q: Find the dimensions of the rectangular box with the largest volume if the total surface area given…

A: It is known that the surfaces area for the rectangular box with edges is x,y and z is 2xy+yz+zx and…

Q: If 1200 cm? of material is available to make a box with a square base and an open top, find the…

A: Given, material available = 1200 cm2 Let's assume the sides of the square base = a Height of the…

Q: A pressure tank has a hemispherical base surmounted by a right circular cylinder and which in turn…

A: Given data: The diameter of all 3 parts of the tank is, r=1.83 m. The altitude of cylinder is,…

Q: Find the dimensions of a rectangular prism whose volume is (x4 ‒  y4) units3.

A: Given that,                volume, v =  (x4 ‒  y4) units3

Q: Find the volume of a regular triangular pyramid if the length of one side of the base is 12 cm and…

A:

Q: Find the dimensions of a rectangle with perimeter 200 ft and whose area is as large as possible. O…

A:

Q: A rectangle has a perimeter of 100 cm. What dimensions will give the biggest area?

A:

Q: If 1,200 cm2 of material is available to make a box with a square base and an open top, find the…

A:

Q: A diagonal of a cube joins two vertices not in the same face. If the diagonals are 4V3 cm long, what…

A: Given: A diagonal of a cube joins two vertices not in the same face. Length of diagonals are 43  cm…

Q: Find the volume of a regular tetrahedron whose edge measures 10 m.

A:

Q: Find the volume of a sphere with a diamater of 8.

A: Volume of a sphere with (diameter=8cm)=? radius of sphere=diamter/2=4cm

Q: A prism has a volume of 213 ft3. what is the volume of a pyramid that has the same base and height…

A:

Q: 12. Find the volume of a right circular cylinder that can be circumscribed about a cube whose…

A:

Q: Find the dimensions of the largest box with a square base that can be cut from a solid sphere of…

A:

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

A:

Q: If 4,800 cm of material is available to make a box with a square base and an open top, find the…

A: Given 4800 cm^2 of material is available to make a box with a square base and an open top

Q: Find the area of a square whose diagonal has length 14.5 cm.

A: The diagonal length of the square is 14.5 cm. we have to find its area.

Q: Calculate the volume of the regular tetrahedron in the figure knowing that its edge AB=1Ocm.…

A: Given data: edge AB= a= 10 cm

Q: Find the dimensions of a box with largest volume whose surface area is 100 cm?.

A:

Q: What is the largest possible volume of a rectangular box whose diagonal has length L?

A:

Q: If 1200cm^2 of material is used to make a box with square base and open top, find the largest…

A: Box is the open top with the square base, let x be its length and width, and h be its height. Then…

Q: what is the edge length of a dodecahedron with a volume of 958 cubic inches

A: Given : volume of dodecahedron is 958 cubic inches . To find the edge length

Q: Find the dimension of the largest side of a rectangular boc that can be fitted to a triangular space…

A: Let △ABC be the required triangle. If we observe the dimensions of the triangle 15 inches, 36 inches…

Q: If 1400 square centimeters of material is available to make a box with a square base and an open…

A: Explained below

Q: A dog trainer has 66 ft of fencing with which to create a rectangular work area for dogs. If the…

A: Given:Perimeter = 66 ftArea = 182 ft2

Q: The base of a right prism is an equilateral triangle whose edges is 10cm each and it lateral edge is…

A:

Q: 6. Find the dimensions of a rectangle with an area of 225 cm’, whose perimeter is as small as…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the dimensions of the rectangular box with largest volume if the total surface area is given as…

A: We have to find

Q: Multivariable optimization question

A:

Q: The owner of a ranch has 1,000 yards of fencing material with which to enclose a rectangular piece…

A:

Q: Find the dimensions of a rectangle with a perimeter of 120 ft that has the largest possible area.

A:

Q: Find the volume of this triangular prism. :)

A: Volume of a triangular prism is calculated by- V=12×b×h×l where b is the base of the prism…