Find the volume of a napkin ring created by drilling a hole of radius r through the center of a wooden sphere of radius R. Remember that the equation of a circle of radius r is x^2+y^2=r^2.

Q: Determine the volume of the rotating object that occurs if the area of ​​the curve y1 = - x2 + 4 and…

A:

Q: The lateral area of a right circular cone is 386 square centimeters. If the diameter is one-half its…

A: Image is attached with detailed explanation.

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

A:

Q: Find the height of the largest volume of a right cylinder that can be inscribed in a right circular…

A: Cone          Cylinder   Radius         r                   x   Height         h…

Q: Matthew is constructing a rectangular prism with volume exactly 720 cubic inches. It will have the…

A: Given Information- Volume of the rectangular prism = 720 in3. The rectangular prism has the least…

Q: Find the volume of this cone shaped object. Height = 6 in Radius = 2 in %3D

A: The volume of a cone of height h and base radius r is given by V=13πr2h

Q: A paint company wants to change the height of its cans of paint to 15 centimeters tall so when the…

A:

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

A: Here volume of the can is equal to the volume of the cylinder. So volume of the can can be expressed…

Q: A semi – circle of radius 14 cm is bent to form a rectangle whose length is 1 cm more than its…

A:

Q: A silo used to store grain can be the modeled as a right circular cylinder with radius 9.5 m and…

A:

Q: A storage tank for butane gas is to be built in the shape of a right circular cylinder of altitude…

A: the volume of the cylinder is given by  v1=πr2h here we have  h=28 feet r=x v1=πx2·28 v1=28πx2

Q: A tumor is approximately sphericalin shape. If the radius of the tumor changes from 14 mm to16 mm,…

A: A tumor is approximately spherical in shape. If the radius of the tumor changes from 14 mm to 16 mm,…

Q: You have 268 feet of fencing to enclose a rectangular region. What is the maximum area of the…

A: maximum area of the rectangle

Q: The lateral area of the right circular cylindrical water tank is 92 sq m and its volume is 360 cubic…

A: Let's find.

Q: Find the dimensions of the right cylinder with largest volume that can be inscribed in a sphere with…

A: We need to find dimensions of cylinder.

Q: An Closed rectangular tank with a squarc base can accommodate 1,922 Cubic feet of water. Find the…

A: According to question, Volume of rectangular tank = 1922 cubic feet

Q: Find the total surface area of the cone whose radius is 70 meters and slant height is 10 meters.

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Q: Find the volume of the largest cylinder that can be inscribed in a right circular cone of radius 3…

A: Solution

Q: Find the dimensions of the right circular cone of greatest lateral area that can be inscribed in a…

A:

Q: This container is composed of a right circular cylinder and a right circular cone. Which is closest…

A: Diameter d= 24 ftRadius r = 242ft    ⇒r = 12 ftheight of cylindrical part h = 10 ftlateral height l…

Q: If a cone has a radius of 4 centimeters and a height of 12 centimeters what is the volume of the…

A: Given Height of the cone h=12 cm Radius of the base of the cone r=4 cm

Q: Find the length of the radius and the altitude of the cylinder of greatest volume if the radius…

A: Find the length of the radius and the altitude of the cylinder of greatest volume if the radius…

Q: Suppose that the radius and height of a cylinder must add to be 15 cm. What radius and height will…

A:

Q: What are the dimensions of an open-top right circular cylindrical can that will hold a volume of 512…

A:

Q: Find the largest volume of a right cylinder that can be inscribed in a sphere of radius 12

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Q: what is the area of circle having a chord with lenght 1.40 cm and 0.60 cm from its center

A: SOLUTION-

Q: The factory designers are currently investigating whether a cone-shaped container can be replaced…

A: let the height of cone is h1  So , A/c the radius of cylinder and cone is same let 'r' and surface…

Q: If you double the length of the radius of a sphere from its original length, what effect does that…

A: Given that: Length of radius of a sphere is doubled.

Q: parabolend=

A: I answered your Question of double integration. I hope u will be benefited from my solutions thank…

Q: Find the volume of the object formed by rotating the area between the square with a side length of 2…

A:

Q: The radius of a cylinder is multiplied by 9 while the height is kept the same. What effect does this…

A: We have to find volume of cone

Q: Find the dimensions of the right circular cylinder of maximum volume that can be inscribed in a…

A: Given, Radius=3 inch Height=10 inch The formula for the volume of a cylinder is, v=πr2h Let, x be…

Q: The volume of a right circular cone is 36π. If its altitude is 2, find its radius?

A: From the given ques  the volume of the right circular cone (v) = 36π and the altiitude (h) = 2 R = ?…

Q: Find the height and radius of a cylinder with volume 250pi in^3 and with the smallest total surface…

A: The volume of the cylinder with radius r and height h is V = 250π in3  ⇒ πr2h = 250π…

Q: calculate the volume of the water inside a 6in radius hemispherical bowl if the height of the water…

A: The volume of water of height h inside a hemispherical bowl with radius R.

Q: Find the dimensions of the rectangle of greatest area that can be inscribed in a circle of radius a.

A: Let x and y be the length and width of the rectangle inscribe in a circle of radius a. Then the…

Q: Find the maximum volume of a rectangular box whose surface area is 1600 cm? and whose total edge…

A: By using lagrange multiplier

Q: Find the maximum volume of a rectangular box with no top that has a surface area of 48 square…

A:

Q: Find the dimentions of a cylinder. See images

A:

Q: Find the minimum amount of thin sheet that can be made into a closed cylinder having a volume of 108…

A: Topic: calculus

Q: A right triangle whose hypotenuse is 15 m long is revolved about one of its legs to generate a right…

A:

Q: should the box have in order to minimize the surface area?

A:

Q: Multivariable optimization question

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Q: if the lateral area of right circular cylinder is 88 and its volume is 220, find its radius

A: A= 88 V = 220 A= 2πrh V = πr²h Now we take ration of volume by area  V/A = πr²h/2πrh r = 2V/A  r =…

Q: Write a formula that estimates the change that occurs in the lateral surface area of a right…

A: Let the radius = rInitial height = h0final height = h0+ dh

Q: Find the dimensions of the right cylinder with largest volume that can be inscribed in a sphere with…

A: We have to find the dimensions of cylinder.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.