Area

Show that the area of the polar sector (see figure) is where is the average radius of

answer

watching

views

For unlimited access to Homework Help, a Homework+ subscription is required.

You have 0 free answers left.
Get unlimited access to 3.8 million step-by-step answers.

Get unlimited access

Already have an account? Log in

Joram GuingguingLv10

10 Oct 2020

Unlock all answers

Get 1 free homework help answer.

Already have an account? Log in

Related questions

Given a circular sector with radius L and center angle (see figure), show that the area of the sector is given by

sapphiremanatee212

Given a circular sector with radius L and center angle (see figure), show that the area of the sector is given by

coralyellowjacket512

Verifying a Formula

(a) Given a circular sector with radius L and central angle (see figure), show that the area of the sector is given by .

(b) By joining the straight-line edges of the sector in part (a), a right circular cone is formed (see figure) and the lateral surface area of the cone is the same as the area of the sector. Show that the area is , where r is the radius of the base of the cone. (Hint: The arc length of the sector equals the circumference of the base of the cone.)

(c) Use the result of part (b) to verify that the formula for the lateral surface area of the frustum of a cone with slant height L and radii r₁ and r₂ (see figure) is .(Note: This formula was used to develop the integral for finding the surface area of a surface of revolution.)