A cylindrical can, open at the top, is to hold 470 cm3 of liquid. Find the height and radius that minimize the amount of material needed to manufacture the can. Enter your answer with rational exponents, and use pi to represent π. Radius =  Height =

Q: A hose has a radius of approximately 0.5 in. and a lengthof approximately 20 ft. By what factor does…

A: Assume radius of the hose be r and length be l. Given, r=0.5 inches and l=20 ft

Q: A rectangular prism has a volume of 8x^3+14x^2+x-2 and a height of 2x+1. Which expression represents…

A: See attached file for a step by step explanation to find the required area of the base of the…

Q: If the pre-image of a shape has an area of 16. What is the area of the image of the scale factor is…

A: Ratio of areas of image and pre-image is equal to square of  scale factor.

Q: If the focal length of a reflection telescope is 200 cm and the focal length of the eyepiece lens is…

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Q: Suppose you could "super-size" the soda can shown below (with diameter 2.5 inches and 4.8 inches…

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Q: One circle has a radius of 8 m, and a second circle has a radius of 10 m. What is the difference in…

A: Let

Q: Make sure you reduce your fraction. Give the value of 1 for y if your answer comes out to a whole…

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Q: ) The length of the box is 9 inches more than its width. The height of the box is 1 inch less than…

A: Given: Length is 9 inches more than width. Height is 1 inch less than width. Volume = 72 inch3

Q: The total area of a cylinder is 90π. If h = 12, find r

A: We know that the total area (A) of a cylinder is: A=2πr2+2πrh where r is the radius and h is the…

Q: The volume of a rectangular box is hB, where h is the height and B is the area of the base of the…

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Q: An open box is to be made from 8 inches by 18 inches piece of cardboard by cutting squares of equal…

A: Let l is length of the box, w is a width of the box and h is the height of the box.…

Q: A concrete pillar has the shape of a cylinder. It has a radius of 4 meters and a height of 9 meters.…

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Q: A tank with rectangular base and sides and open at the top, is to be constructed so that its depth…

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Q: The height of the cylinder below is 4.5 centimeters and the volume is 40.5pi cubic centimeters what…

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Q: write a formula that expresses a volume V of the cube in terms of its side length X

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Q: Starting with a 200-foot long stone wall, a farmer would like to construct a rectangular enclosure…

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Q: The area of a circle circumscribing about an equilateral triangle is 400 sq. m. What is the area of…

A: Given that area of the circle= 400 sq.m. We find area of the triangle.

Q: The rectangular tank shown here, with its top atground level, is used to catch runoff water. Assume…

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Q: Starting with a 40-foot-long stone wall, a farmer would like to construct a rectangular enclosure by…

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Q: Solve for the radius of a sphere if the volume is 268.08 and the length of the radius is x+ 4. 12 6.

A: Given volume of the sphere, V=268.08 unit3 And the length of the radius, r=x2+4...(1) To solve for…

Q: The base of a right prism is a rectangle. If the rectangle has dimensions 2 x 3, and the prism has a…

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Q: Calculate the height that we can reach with a 3m ladder leaning against a wall if the bottom of the…

A: First we consider a triangle ABC, in which the height of AB = a, BC = 3m and AC = 7 cm So, the…

Q: 3 The volume of the rectangular right prism alongside is 48 cm³, the length is 2x cm, the width is x…

A: A right rectangular prism is a solid three dimensional prism with the angle between two edges is…

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

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Q: A cylinder has a height of 12 in. and a radius of 4 in. How can you change the radius of the…

A: Given the height of a cylinder h=12inch and radius of the cylinder r=4inch We need to find the…

Q: An open-toped rectangular dumpster that is twice as long as it is wide and can hold 12y cubic yards…

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Q: Suppose that the volume of an aluminum can is to be 97 in. Find the dimensions of the can if the…

A: given: the volume of an aluminium can is 9π in3. we have to find the dimensions of the can if the…

Q: A parabolic goblet with a cup that is as wide as it is tall holds 1.74r^3 oz of water when it is…

A: A parabolic goblet with a cup that is as wide as it is tall holds 1.74r3 oz of water when it is…

Q: Calculate the amount of concrete required to cover the curved part of a pipe with a diameter of 50…

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Q: The Luxor Casino in Las Vegas is a square-based pyramid. The height of the pyramid is 350 ft and the…

A: The objective is to find the air capacity that the building can hold.

Q: Reba says that if she takes a block of modeling clay and makes different shapes with it, the surface…

A: It is true, because as long as the same block of clay is used, the total area available doesn't…

Q: An open-toped rectangular dumpster that is twice as long as it is wide and can hold 12y cubic yards…

A: Given:An open-toped rectangular dumpster that is twice as long as it is wide and can hold 12y cubic…

Q: The area of the base of a prism can be expressed as x2 + 4x + 1 and theheight of the prism can be…

A: Volume of any solid is given by multiplication of base area and height.

Q: The volume of a cylinder can be expressed as V = rr²h, whereris the radius, and h is the height of…

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Q: The radius and height of a cone are reduced by the same factor of 6. If the original surface area…

A: Topic- surface area of cone

Q: Starting with a 60-foot-long stone​ wall, a farmer would like to construct a rectangular enclosure…

A: So perimeter of the fence = x+w+60+x+w= 480 feet So,

Q: Suppose 2700 cm² of material is available to make a box with a square base and open top. a) Show…

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Q: A waste management company is designing a rectangular construction dumpster that will be twice as…

A: Given, volume of dumpster= length(l) ×base(b)×height(h) from given condition b=x, l=2x, h=x…

Q: what is the maximum volme of water a hampster bath could hold with a depth of 1 2/3 inches , a…

A: Given that  length=213inches width=2 inches  depth=123 inches  find the volume  volume=length x…

Q: The shape of a Norman window can be approxiamated by a rectangle with a semicircle on the top. What…

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

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Q: A gutter with trapezoidal cross section is to be made from a long sheet of tin that is 15 inches…

A: Trapezoidal  and geometrical area

Q: Q.1: The length of rectangular piece of paper exceeds its breadth by 5cm. If a strip of 0.5cm wide…

A: The area of a rectangle is equal to the product of its length and breadth. Let the length and the…

Q: The sphere below on the left has a radius r = 3 cm. If the sphere is enlarged by a factor of 4, how…

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Q: Starting with a 20-foot-long stone wall, a farmer would like to construct a rectangular enclosure by…

A: Introduction: Consider the function f ( x ) with one variable. Using derivatives, the function…

Q: A cone has a volume that is 350 cubic meters. What is the volume of a similar cone that is twice as…

A: Given, Volume of 1st cone = 350 cubic meters To find the volume of a similar cone that is twice as…

Q: the total area of a cone is 125 pi cm^2 if its dimensions are increased to five times their original…

A: The total area of cone is A=πrr+l where r is the radius and l is the slant height.

Q: A waste management company is designing a rectangular construction dumpster that will be twice as…

A: Explanation of the answer is as follows

Q: Suppose you ask a jeweller to form a gold in the shape of a sphere whose volume is * cm³. But you…

A: Intial volume of gold = 4π/3.

Q: You reduce in size a large sphere with surface area of 169TT cm2 to become a sphere with surface…

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