7. The volume of a certain rectangular prism is (2x3+ x2-22x + 24) cubic units. If the height is (2x-3) units, what is the area of the base?

Q: 2 towns A and B are situated 3km and 4km from a main road as shown in the diagram. Where should the…

A: Let J is x km away from point C. So JD=6-x

Q: 3. A rectangular pea patch with total area 128 m² is to be enclosed by a fence and divided into…

A: Consider the given rectangular pea patch with dimensions x m by y m. The area of the rectangular pea…

Q: 3. Find the dimension of the largest rectangle (in terms of area) that can be inscribed in a circle…

A: To Find: the dimension of the largest rectangle ( in terms of area) that can be inscribed in a…

Q: A campground owner plans to enclose a rectangular field adjacent to a river.The owner wants the…

A: A campground owner plans to enclose a rectangular field adjacent to a river. The owner wants the…

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: 19. What is the volume of a square pyramid whose length of one side of its base is 9 cm and whose…

A: Volume of pyramid problem.....

Q: 3. A farmer has 1,200 meter of fencing and wants to fence off a rectangular field that borders a…

A:

Q: 1. Find the area of the largest circle which can be cut from a square of edge 5in. What is the area…

A:

Q: 5.) A box is to be constructed from a square piece of zinc with side 40 in by cutting equal squares…

A: Explanation of the answer is as follows

Q: A cube has an edge of length 30. A rectangular solid has edge of lengths 20, 30 and L. If the cube…

A: Given: A cube has an edge of length 30. A rectangular solid has an edge of lengths 20, 30 and L.…

Q: 2. A printer needs to make a campaign poster that will have a total area of 200 in? and will have…

A:

Q: 20.) If the radius and height of a cylinder are both doubled, then the surface area is.. a. the same…

A: Let r be the radius and h be the height of the cylinder then surface area of the cylinder is given…

Q: Suppose that postal requirements specify that parcels must have length plus girth at most 84 inches.…

A: Length + girth = 84 inches. Here, length = h girth = 4x so, we write h+4x=84.........(1)

Q: 7. If a cylinder has a surface area of 60 square inchess and a diameter of 3 inches, what is its…

A: Given :  Surface area of cylinder = 60 sq. Inches Diameter (2r ) = 3 inches

Q: 4. A water tower is built in the shape of a right circular cylinder whose base is 10 meters in…

A: The tower is built in the shape of a right circular cylinder with base diameter 10 meters and…

Q: Suppose that we want to send a parcel in the shape of a square-based rectangular solid, and the…

A: Given that the base is square shaped. Let x be the dimension of one side of the base. Then, girth =…

Q: 6. Calculate the area of a regular octagon, if each side is 5 cm and the width across the flats is…

A: Consider the following figure. The area of the above octagon is 8 times the area of the triangle…

Q: b) A printer need to make a poster that will have a total area of 2000 cm? and will have 3 cm…

A:

Q: 5) An aquarium tank in the shape of a rectangular prism is 20 inches long by 16 inches wide by 12…

A: The tank dimensions are  Length l = 20 inches Width b = 16 inches Height h = 12 inches

Q: Suppose that the base of the square pyramid below has an area of 12 cm2 and that the altitude of the…

A:

Q: 1. What is the volume of a cube whose edges are (4a + 3) cm in length? A. 64a³ – 48a² + 36a − 27 ??³…

A:

Q: 13 Find the area of the rectangle of largest area that can be inscribed in a semicircle of radius 6.

A: We first consider a semicircle with center at (0,0) and radius = 6  It will have equation:

Q: 2. You are planning to make an open rectangular box from an 8 cm x 15 cm piece of cardboard. You…

A: An open rectangular box is made from a cardboard.we need to find the dimensions of largest box that…

Q: 1. A supermarket employee wants to construct an open-top box from a 14 by 30 in a piece four corners…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: 5. A sheet of cardboard 3 ft by 4 ft will be made into a box by cutting equal-sized squares from…

A: The volume of the box can be obtained using the formula v=l×w×h. Here, l is the length , w is width…

Q: 7. The top and bottom margins of a poster are each 6 cm and the side margins are each 4 cm. If the…

A:

Q: 3. If a trapezoid has an altitude of 15 inches, an area of 105 square inches, and one of the bases 5…

A:

Q: If the area of the base of the octagonal pyramid is 553.12 square feet and the height of the pyramid…

A: The formula for the volume of an octagonal pyramid is one-third of the product of the area of the…

Q: 1. Find the total area and volume of frustum of regular square pyramid, whose base have sides 10 cm…

A:

Q: If a cube has a volume of 64. What is it’s edge length

A:

Q: 14. City college is having a poster contest. The posters must be rectangular in shape, and they must…

A:

Q: 3. The cross-section of a tunnel, 50 meters in length is in the form of a rectangle 8 m wide and 4 m…

A:

Q: 6. Find the difference of the areas of a square and a semi-circle if the square is inscribed in the…

A:

Q: What are the dimensions of the lightest​ open-top right circular cylindrical can that will hold a…

A:

Q: 8. The Toronto Zoo wishes to construct an aquarium in the shape of a rectangular prism such that the…

A:

Q: 13. Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral…

A:

Q: Suppose that we want to send a parcel in the shape of a square-based rectangular solid, and the…

A: Let each side of the square base of the box be x inches and the length of the box be l inches…

Q: 1. A 216-m² rectangular patch is to be enclosed by a fence and divided into two equal parts by…

A: To find the material needed.

Q: 2. If the edge of a cube is 1.75 m, then how many square centimeters are there in its entire…

A: Given :  Edge of Cube =a=1.75 m To find : surface area of cube in square centimeters

Q: 2. A rectangular field has a length of 120 m and a width of 300 ft. What is the area of the field in…

A:

Q: 9. Find the dimensions of the rectangular box with largest value if the total surface area is given…

A: To find The dimensions of the rectangular box

Q: 13. Find the dimensions of a rectangle with area 1000 m² whose perimeter is as small as possible.

A: Given: Area of the rectangle is 1000 m2.

Q: 5. The height of the cube toy box of Terence is 4x? - 3y?, If the volume of the cube is 64x* -27y,…

A: Given:- The height of the cube toy box of Terence is 4x2 -3y². If the volume of the cube is 64x6…

Q: 9. Find the area of the largest rectangle that fits inside a circle of radius 10.

A:

Q: 2. Among all rectangles that have perimeter of (54+0) ft, find the dimensions of the one with…

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: Base length of pyramid:= 4.5 in Width of pyramid:= 7 in Height of pyramid:= 16 in   Now:          If…

Q: 2. Find the lengths of all sides of the right triangle below if its area is 400. 2x

A: Topic:- Geometry  X=20 2X =40 H =20√5

Q: 2. A rectangle has an area of 100 m?. Find the dimensions of the rectangle that yields the smallest…

A: Given the area of a rectangle is: Now, Formula used : Let the length and breadth of the rectangle…

Q: 2. A rectangular sheet of cardboard 8 m by 4 m is used to make an open box by cutting squares of…

A: Volume of cube = a3Volume of cuboid =l×b×hWhere l is length , b is breadth and h is height .