An open box is to be made from a thirty-inch by thirty-inch square piece of material by cutting equal squares from the corners and turning up the sides (see figure). 30 – 2 x 30 – 2x Find the volume of the largest box that can be made.

An open box is to be made from a thirty-inch by thirty-inch square piece of material by cutting equal squares from the corners and turning up the sides (see figure). 30 – 2 x 30 – 2x Find the volume of the largest box that can be made.

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter1: Equations, Inequalities, And Mathematical Modeling

Section1.4: Quadratic Equations And Applications

Problem 108E: Geometry You construct an open box from a square piece of material by cutting four-centimeter...

See similar textbooks

Related questions

Q: A window consists of rectangular pane of glass surmounted bya semicircular pane of glass (see…

A: Given: Perimeter of the window is 20 feet. Consider height is y and diameter of the semicircle is x.…

Q: A frame for a picture is 2 inches wide (see figure). The picture inside the frame is 4 inches longer…

A: As shown in the figure, the Frame has a 2-inch border on each side,

Q: Factor the perfect square. x2 + 10 x + 25

A: Consider the provided perfect square, x2+10x+25 Find the factor of the perfect square.

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A: Solution

Q: You are constructing a cardboard box from a piece of cardboard with the dimensions 4 m by 8 m. You…

Q: 10) A norman window has the shape of a rectangle surmounted by a semicircle (similar to older…

Q: 10. A Norman window is constructed by adjoining a semicircle on the top of an ordinary rectangular…

Q: Enclosing the Largest Area grazing land along the straight portion of a river and then subdivide it…

Q: 91. Maximizing an Enclosed Area A farmer with 2000 meters of fencing wants to enclose a rectangular…

Q: The white square in the drawing below is located in the centre of the grey rectangle and has a…

Q: 5. An open-top box is to be made by cutting squares from a sheet of tin 4 ft. long and 2.5 ft. wide…

A: 5. Given that, An open-top box is to be made by cutting squares from a sheet of tin 4 ft. long and…

Q: A rectangle with a solid edge is 90 wide and 30 tall. A square is at each corner. The length and…

A: Area of rectangle = length x width Volume of rectangular container = length x width x height Given:…

Q: An open rectangular box is to be made from a piece of cardboard 8 inches wide and 15 inches long by…

Q: A box with square ends of side x and a length L is to be made such that L+4x = 4 meters. The…

Q: Express the give quantity in terms of the indicated variable.

A: Express the give quantity in terms of the indicated variable.

Q: 20 cm 12 cm

A: given in a cylinder,radius (r)=12cmheight(h)=20cmthereforesurface area…

Q: A sheet of cardboard 3 ft. by 4 ft. will be made into a box (no top) by cutting equal-sized squares…

Q: A rectangle whose length is x and whose width is less than its length by 2 The perimeter of the…

Q: The white square in the drawing below is located in the centre of the grey rectangle and has a…

Q: A farmer wants to enclose two adjacent goat pens beside his barn (see figure below). The wall of the…

Q: The volume of a rectangular box is x3 + 16x2 + 83x + 140 cm³. The box is (x+5) cm long and (x+7) cm…

Q: An Open Box A rectangular board is 6 in longer than its width. An open box was made by cutting 3 in.…

Q: A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular…

Q: Enclosing the Largest Area The owner of the Rancho Los Feliz has 2580 yd of fencing to enclose a…

A: The owner of the Rancho Los Feliz has 2580 yd. of fencing to enclose a rectangular piece of grazing…

Q: A rectangular frame needs to have an opening of 28 square inches. The boards used to create the…

Q: a) Find the volume of the shaded figure by subtracting the smaller volume from the larger. The…

Q: 3 5. The volume of the cube shown is x³ – 5x2 + 6x if one of the dimensions is x, which represents…

A: x3-5x2+6x⇒xx2-5x+6⇒xx2-3x-2x+6⇒xx-3x-2

Q: A sculptor removes a pyramid from a block of wood shaped like a square prism with the same base and…

A: It is given that, a pyramid is extracted out from a wooden block with same base and height. So, all…

Q: the number of hours worked and an employee's wages 25. Find the three factors for possible…

Q: find the area of the largest rectangle that can be inscribed in a triangle with dimensions10m 12m…

Q: A rectangle has a perimeter of 46 centimeters and an area of 120 square centimeters. Find the…

A: The perimeter and area of the rectangle are given as 46 centimetres and 120 square centimetres…

Q: 19. A rectangle has a length of 12x²y and a width of 6xy. a. What is the area of the rectangle? b.…

A: A detailed solution is given below.

Q: A trapezoid has a height of (x + 2)cm and the length of two opposite parallel sides are (x + 4)cm…

Q: feet. The fence along three sides is to be A fence is to be built to enclose a rectangular area of…

Q: Construction A box is being constructed by cutting 2-inch squares from the corners of a square sheet…

A: given: A box is being constructed by cutting 2-inch squares from the corners of a square sheet of…

Q: Enclosing the Largest Area The owner of the Rancho Los Feliz has 3540 yd of fencing to enclose a…

A: Given : Fencing is equal to 3540 yd . To find : Value of x & y and area of rectangular piece of…

Q: A rectangle has a perimeter of 36 in. The length and width are scaled by a factor 2.5. What is the…

A: Given that perimeter of a rectangle is 36 inches The formula of the perimeter of the rectangle P…

Q: An artist creates a carving from a rectangular block of soapstone whose volume, V , can be modelled…

Q: 7. The area of a rectangular piece of cardboard shown is 675 square inches. The cardboard is used to…

Q: Parcel Post Regulations Postal regulations specify that a parcel sent by priority mail may have a…

Q: The white square in the drawing below is located in the centre of the grey rectangle and has a…

Q: 1. At math camp the lap pool is a rectangle that is (x2 – 16)ft by (x + 3)ft, the wading pool is a…

Q: The volume of a cubic storage bin is (125x 3 – 64) m 3 . Express the volume in factored form.

Q: 9. MNOP is a square. Find the following: 9. m<N3D perimeter of MNOP = 3x + 14 area of MNOP = NO = O.…

A: There are multiple question, So as per Bartleby Policy Kindly ask multiple question separately.…

Q: The volume of a rectangular prism is 20 cm. When the length of the prism is multiplied by a scale…

Q: Enclosing the Largest Area The owner of the Rancho Los Feliz has 3420 yd of fencing to enclose a…

A: To find the dimensions

Q: A rectangular garden has an area of 735m2. If length is decreased by 7m and breadth is increased by…

Q: 2. Explain how to find the area of the shaded region in the figure, if the length and the width of…

A: We will solve the following

Q: The area of a rectangle is the product of the length and the width, or Consider the rectangle below.…

A: The given question is related with the area of a rectangle. Given a rectangle with length, L = x +…

Q: 9. A rectangle has length (3x + 5) cm and width (2x – 1) cm. What is the area of the rectangle? a 5x…

Question

An open box is to be made from a thirty-inch by thirty-inch square piece of material by cutting equal squares from the corners and turning up the sides (see figure).
30 – 2 x
30 – 2 x
Find the volume of the largest box that can be made.
V =
in3

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Area$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

Geometry You construct an open box with a square base (see figure) from 108 square inches of material. The height of the box is 3 inches. What are the dimensions of the box? (Hint: The surface area is S=x2+4xh.)
Dimensions A rectangular picture frame has a perimeter of 3 meters. The height of the frame is 23 times its width. Find the dimensions of the picture frame.
Geometry You construct an open box from a square piece of material by cutting four-centimeter squares from the corners and turning up the sides (see figure). The volume of the box is 576 cubic centimeters. Find the dimensions of the square piece of material that you use to construct the box.
Enclosing a field You have 16 miles of fence that you will use to enclose a rectangle field. a.Draw a picture to show that you can arrange the 16 miles fence into a rectangle of width 3 miles and length 5 miles. What is the area of this rectangle? b.Draw a picture to show that you can arrange the 16 miles fence into a rectangle of width 2 miles and length 6 miles. What is the area of this rectangle? c.The first two parts of this exercise are designed to show you that you can get different areas for the rectangle of the sane perimeter, 16 miles. In general, if you arrange the 16 miles of fence into a rectangle of width w miles, then it will enclose an area of A=w8-w square miles. iMake a graph of the area enclosed as a function of w, and explain what the graph is showing. iiWhat width w should you use to enclose the most area? iiiWhat is the length of the maximum-area rectangle that you made, and what kind of figure do you have?
Page Design A rectangular page contains 64square inches of print. The margins at the top and bottom of the page are each 1inch deep. The margins on each side are 112inches wide. What should the dimensions of the page be to use the least amount of paper?
Length of a Tank The diameter of a cylindrical propane gas tank is 4 feet. The total volume of the tank is 603.2 cubic feet. Find the length of the tank.