In this problem we will show that the volume of a right cone of radius r and height h is given byr2²h3π-(a) Give an expression for the volume of the cone in terms of the integral of a two-variablefunction over a region of the plane (there are several ways to do this).(b) Compute the integral to establish the formula.h

(a) To Write: Integral as function of two variables for the volume of the cone. (b) To Evaluate: The…

Answered: In this problem we will show that the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(b) A cake is shaped like a hemisphere of radius 2 with base on the ry-plane. A wedge of cake is removed by making two cuts from the center of the cake outward, perpendicular to the ry-plane and separated by an angle of p. (b1) Use a double integral to find the T volume of the slice for = = 4
Find the volume of a ball of radius R with the top cap of height h is removed. You should assume ŉ is measured along a diameter of the ball and h < R.
i need someone to help me. when i graph and draw discs, they only touch the absolute value of x. how do i set up Big raidus and small raduis within the intergal
Find the surface area of the solid generated when the segment of the graph of x =ln(cosy) for 0≤ y ≤ pi/ 3 is rotated about the y-axis. Set up the integral showing all your steps and then integrate on the calculator
We are going to walk through two ways to derive the volume of a right circular cone. To do so, we start by considering the line y = ;x. We then consider the region bounded by this line and the lines y = 0 and x = h - note that this is a right triangle with base h and height r. The idea is that if we rotate this region about the x axis, we will get a filled-in right circular cone with radius r and height h.
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A pool in the shape of a hemisphere with a radius of 7 feet is filled with 6 feet of water. Letting yy be the distance from the bottom of the hemisphere, set up the integral that would be used to find the total amount of work done in pumping the water to a point 5 fet above the top of the pool.
Please explain steps in details: The function y = x^2 from x = 0 to 2 is rotated about the y-axis. 1) Find the volume of the resulting solid 2) If the resulting solid is filled with water, find the work done in emptying it – assume all units ofmeasurement are in meters. 3) Find the surface area of the resulting shape (set up the integral, and find a numerical approximation)

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