25) From a thin piece of cardboard 10 in. by 10 in., square corners are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Round to the nearest tenth, if necessary.

25) From a thin piece of cardboard 10 in. by 10 in., square corners are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Round to the nearest tenth, if necessary.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.1: Prisms, Area And Volume

Problem 39E: Kristine creates an open box by cutting congruent squares from the four corners of a square piece of...

See similar textbooks

Related questions

Q: The volume of a frustum of a regular triangle pyramid is 135 cu. m. The lower base is an equilateral…

Q: A sphere with a radius of 3 in. is repeatedly filled with water and emptied into a cone with a…

A: We need to find how many times how many times sphere emptied into the cone.

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: a sphere inscirbed in a right circular cone whose slant height has a length equal to the diameter of…

Q: A rectangular piece of metal is 20 in longer than it is wide. Squares with sides 4 in long are cut…

A: Topic - application of quadratic equations

Q: The volume of the frustum of a regular triangular pyramid is 135 cu m. The lower base is an…

Q: 1. Find the volume and total area of a rectangular parallelepiped which is 15 ft high and the side…

A: Explanation of the answer is as follows

Q: 9. Suppose that each of the bases of the hexagonal prism in Exercise 1 has an area of 12 cm2 and…

A: 9. The formula for the volume of a regular prism is given as follows:

Q: 4. A manufacturer wants to design an open box having a square base and a surface area of 1200 cm2.…

A: Given: A manufacturer wants to design an open box having a square base and a surface area of 1200…

Q: 7. If 300 cm³ of material is available to make a box with a square base and an open top, find the…

A: Assume side of the square box is x and height is y. Hence, volume of the box is given by…

Q: 4. The altitude of a right hexagonal prism is twice as long as the edge of the base. If the prism…

A: Given Volume = 1923in3

Q: 1. If the cube has a side lenght of 1 unit, what is the volume 2.) What is the surface area of the…

A: volume = no of cube*(volume of 1 cube) volume = 44*(1*1*1) volume = 44 unit3 now for surface area =…

Q: 3. Find the area of the base of a regular square pyramid whose lateral faces are equilateral…

A: Solution by pythogoras theorem

Q: . A box with an open top is to be constructed from a square piece of cardboard, 3 m wide, by cutting…

Q: 2. A snowcone with a radius of 4 cm is sold in a cone-shaped paper cup with a height of 12 cm and an…

A: Snowcone is a crunchy ice ball. If r is the radius of any spherical shape body then its volume is…

Q: As in Exercise 39, find the volume of the box if four congruent squares with sides of length 6 in.…

A: We have, a rectangular piece of poster board having dimension 20 inch wide and 30 inch long. Four…

Q: 15. If 1200 cm²? of material is available to make a box with a square base and an open top, find the…

Q: A container with square base, vertical sides, and open top, is to be made from 3,000 ft² material.…

A: This question is based on application of derivative.

Q: If the total surface area of a solid right circular cylinder is 200pi sq. cm. and its radius is 5cm,…

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

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: 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: 35.) What is the volume of a square pyramid with a base edge of 14 m and a slant height of 25 m?

Q: (8) If 1200 cm? of the material is available to make a box with a square base and an open top, find…

A: The volume of the box V=a2h

Q: An open rectangular box with square base is to be made from 48 ft.2 of material. What dimensions…

Q: Suppose an open box with a rectangular base is to be constructed from a rectangular piece of…

Q: A sphere is inscribed in a right circular cone whose slant height has a length equal to the diameter…

A: Given: A sphere is inscribed in a cone whose slant height equal to diameter =12 cm

Q: 1. A box with an open top is to be constructed from a square piece of cardboard 3 ft- wide by…

Q: 10. A right pyramid has a square base and a lateral area of 144 in?. If the slant heights is twice…

Q: Suppose that each of the bases of the triangular prism in Exercise 2 has an area of 3.4 cm? and that…

A: Consider the given: Find the volume of Prism: The Volume of Prism = Base Area ×height It is given…

Q: Suppose that each of the bases of the hexagonal prism in Exercise 1 has an area of 12 cm² and that…

A: Given: The area of each bases of a hexagonal prism is, Abase=12 cm2. The altitude of the hexagonal…

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

Q: If 1200 cm² of material is available to make a box with a square base and an open top, hnd the…

A: Total area is given so first let the base length is a and height is h .. then make the relation of…

Q: Given that a right cireular cylinder is inscribed within a sphere, what is the least possible volume…

A: Given: A right circular cylinder is inscribed within a sphere with the radius r as given in the…

Q: If 10,800 cm2 of material is available to make a box with a square base and an open top, find the…

A: Let length be x cm and height be y cm.The amount of material is equal to surface area.Surface area =…

Q: 1. find the dimenstors of a maximum Lwithout a top of capacity, 108 sq. cm. box who de Sunface area

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

Q: |1. A poster is to have an area of 900cm² with 3cm margins at the bottom and sides and a 5cm margin…

Q: 8. Find the VOLUME of the pyramid that I'm looking at. It is 147 m on each side and 139 m high

Q: A box with an open top is to be constructed from a square piece of cardboard, 24 inches wide, by…

Q: A square base prism and a cylinder both have the same height of 4 cm in the same base area if the…

Q: A sphere is inscribed in a right circular cone whose slant height has a length equal to the diameter…

A: Given:

Q: 1. A box with an open top is to be constructed from a square piece of cardboard 3 feet wide by…

A: Introduction: The volume o the cuboid of side lengths a, b, c is given by, V=a×b×c

Q: What is the smallest perimeter possible for a rectangle whose area is 16 in2, and what are its…

A: Let l be the length and b be the breadth of the rectangle.

Q: Given that a right circular cylinder is inscribed within a sphere, what is the least possible volume…

Q: If a cone has a SA (Surface Area) of 25 and its dimensions are doubled what is the new SA?

A: The surface area of a cone is given by the expression A=πrr+h2+r2. Here, r is the radius of the cone…

Q: 6. If 1200 em of material is available to make a box with a square base and open top, find the…

Q: A caterer wishes to serve a cocktail in a glass shaped like a cone of diameter 8 cm and height 4 cm…

Q: If 4,800 cm2 of material is available to make a box with a square base and an open top, find the…

Question

25) From a thin piece of cardboard 10 in. by 10 in., square corners are cut out so that the sides can be folded up to
make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Round to
the nearest tenth, if necessary.

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

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Trending now

This is a popular solution!

Step by step

Solved in 7 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Prisms$

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

As in Exercise 39, find the volume of the box if four congruent squares with sides of length 6 in. are cut from the corners of a rectangular piece of poster board that is 20 in. wide by 30 in. long. Kristine creates an open box by cutting congruent squares from the four corners of a square piece of cardboard that has a length of 24 in. per side. If the congruent squares that are removed have sides that measure 6 in. each, what is the volume of the box formed by folding and sealing the flaps?
The surface of a soccer ball is composed of 12 regular pentagons and 20 regular hexagons. With each side of each regular polygon measuring 4.5 cm, the area of each regular pentagon is 34.9 cm2 and area of each regular hexagon is 52.5 cm2. a What is the surface area of the soccer ball? b If the material used to construct the ball costs 0.8 of a cent per square centimeter, what is the cost of the materials used in construction?
For a right circular cone, the slant height has a measure equal to twice that of the radius length of the base. If the total area of the cone is 48in2, what are the dimensions of the cone?
A calendar is determined by using each of the 12 faces of a regular dodecahedron for one month of the year. With each side of the regular pentagonal face measuring 4cm, the area of each face is approximately 27.5 cm2. a What is the total surface area of the calendar? b If the material used to construct the calendar costs 0.8 of a cent per square centimeter, what is the cost of the materials used in construction?
Kristine creates an open box by cutting congruent squares from the four corners of a square piece of cardboard that has a length of 24 in. per side. If the congruent squares that are removed have sides that measure 6 in. each, what is the volume of the box formed by folding and sealing the flaps?
If the tank in Exercises 41 needs to be painted and 1 pint of paint covers 50ft2, how many pints are needed to paint the exterior of the storage tank? A cylindrical storage tank has a depth of 5 ft and a radius measuring 2 ft. If each cubic foot can hold 7.5 gallon of gasoline, what is the total storage capacity of the tank measured in gallons?