An open-top box is to be made by cutting small congruent squares from the corners of a 12-in.-by-12-in. sheet of tin and bending up the sides. How large should the squares cut from the corners be to make the box hold as much as possible?

Q: A poster is to have an area of 180 in^2 with 1-inch margins at the bottom and sides and 2-inch…

A:

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

A:

Q: A tinsmith wants to make a small windowsill planter from a 40cm×16cm40⁢cm×16⁢cm sheet of copper.…

A: We will calculate height first from given ratio in question. PFA Given dimension of sheet 40 cm×16…

Q: What is the length of the diagonal of a rectangle given the dimensions are 8 ft by 5 ft? Round to…

A: Given: Dimension of rectangle = 8 ft x 5 ft

Q: 1. A gutter with trapezoidal cross section is to be made from a long sheet of tin that is 18 inches…

A:

Q: Suppose you have a rectangular pyramid with a base length of 4.5 in, a width of 7 in, and a pyramid…

A: To find: The changes in the volume after changing base length and width. Given: The rectangular…

Q: A room in the shape of a triangle has sides of length 6 yd, 8yd, and 13 yd. If carpeting costs…

A:

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: For a right circular cone, the slant height has a measure equal to twice that of the radius length…

A: Given a right circular cone. Whose total area is 48π in2. Slant height=Twice of radius. Let, For…

Q: An open box is to be made from a 16 cm by 30 cm piece of cardboard by cutting out squares of equal…

A: according to our guideline we are supposed to answer only the first question if we want any…

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

A:

Q: A piece of tubing 6 3/16 in. long is to be cut from a piece 24 1/2 in. long. Allowing 1/16 inch for…

A: Since, the length of tubing piece to be cut is 6 3/16 inches. And the total length of tubing is 24…

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

A:

Q: A factory is to be built on a lot measuring 100 ft by 240 ft. A local building code specifies that a…

A: Solving this question, we can construct a quadratic equation that represent the situation. We can…

Q: A pool measuring 10 meters by 20 meters is surrounded by a path of uniform width, as shown in the…

A: Given a pool measuring 10 meters by 20 meters is surrounded by a path of uniform width and area of…

Q: What is the area of a regular pentagon with an apothem of 25.1mm and a side length of 36.4mm?

A: Given that a regular Pentagon with an apothem of 25.1mm and side length of 36.4mm Here we have to…

Q: Find the area of a regular pentagon with a perimeter of 40 feet. Round your answer to the nearest…

A:

Q: A side of an equilateral triangle is 26 yd long. What is the area of the triangle? Do not round any…

A:

Q: Find the area of a regular pentagon with an apothem of 8.95 cm and a side length of (round to the…

A: In the question it is asked to calculate the area (A) of pentagon and side length (L) using the…

Q: The area of a trapezoid is 42 in^2. What is the new area of the trapezoid if the height were tripled…

A:

Q: If an open box is made from a square tin sheet 12×12 in. by cutting an identical squares from each…

A: in this question, there is an open box made by 12*12in  tin sheet For the box to be of the largest…

Q: From a 15-cm by 15-cm piece of cardboard, square cormers are cut out so that the sides can be folded…

A:

Q: A company makes square-pyramid-shaped tents with a height of 6 feet and a base with a side length of…

A:

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: A cylinder of clay has a diameter of 12 cm and a height of 12 cm. If this clay is made into…

A:

Q: A side of an equilateral triangle is 16 m long. What is the area of the triangle? Do not round any…

A: We need to find area of triangle.

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 that length of canvas % meters wide is required to make a conical tent 8 meters in diameter and…

A: Canvas will be on the curved surface area of the tent.   The curved surface area of the conical tent…

Q: 15. Find the length of the second base of a trapezoid with one base measuring 29 ft, a height of 9…

A:

Q: Given a square whose side is denoted as 3(x+4)² cm. What is the diagonal length (in) of the square…

A: As we haven't mentioned which question to solve. So, I am solving first question. Given: A square…

Q: A triangular prism has a rectangular edge of 45cm and volume of 90cm^3. It is cut into identical…

A: Given, Edge of the triangle prism = 45 cm Volume = 90 cm3 Volume of the small prism = 10 cm3

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: A developer wants to subdivide a rectangular plot of land measuring 600 m by 750 m into congruent…

A:

Q: A silo consists of a right circular cylinder surmounted by a hemisphere. Find the most economical…

A: The question is to find the proportions of the silo such that the total cost for making the silo is…

Q: 4. The volume of the fish tank needs to be tripled. 10 in 3 in 18 in What scale factor should be…

A: Given a fish tank whose volume has to be tripled. To find the scale factor

Q: Given a sphere with a diameter of 10 cm, find its volume to the nearest whole number.

A:

Q: The dimensions of a pasta box are 14in by 1.5 in by 3 in. what is the surface area of the box?

A:

Q: A picture frame is in the shape of a square with a circle removed from the centre. If the radius of…

A: Given, a picture frame is in the shape of a square with a circle removed from the centre. if the…

Q: A cube has a volume of 512 in3. Wht is the length of each side of the cube?

A:

Q: A project requires 84 concrete blocks, each of which is a cube measuring 14" by 14" by 14". How many…

A:

Q: A manufacturer has an order for 20,000 megaphones. The megaphones, conical in shape, are to be 2…

A: This question is about a conical object formation. So, we have to use volume formula of cone having…

Q: Find the largest volume of a rectangular box with no top made by cutting little squares out of the…

A:

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

A:

Q: Suppose an oil pan has the rectangular dimensions 14 in. by 16 in. by 3 in. Find its volume (in…

A: From the given information, it is observed that the dimension of oil pan is 14 in. × 16 in. × 3 in.…

Q: The outer circle of the driveway has a diameter of 30 feet and the inner circle of the driveway has…

A: Area of circle

Q: A lead pencil whose ends are regular hexagons was cut from a cylindrical piece of wood, with the…

A: It is given that the diameter of the cylindrical piece of wood is 0.5 in. Then the side length of…

Q: A room in the shape of a triangle has sides of length 6 yd, 8 yd, and 13 yd. If carpeting costs…

A:

Q: Mary Frances has a rectangular garden plot that encloses an area of 48 yd?. If 28 yd of fencing are…

A: Given: The area of a rectangular garden is 48 yd2. For fencing the garden the length required is 28…

Q: A new park design uses part of a city block, but there is already a building in the northwest corner…

A: Area of park = Total Area - Area of Building