Question

) An artist has designed a curved planter that has a flat top and bottom. The sh daying on its side) can be modeled by the function fx) 4911 x planter for -75 s x s 92, where x is in 23 10,000 centimeters. Find the volume of the planter. Example planter on flat surface

Answer 1

We can obtain the volume by rotating the curve over the x-axis.

The volume is an integral

Area()dax

Where Area(x) is the area of a circle whose radius is given by the curve f(x).

So

$Area(x)=\pi radius^2=\pi [f(x)]^2$

Then the volume is

92 ㄒㄧ 49V1-1000 dr 75 92 ㄒㄧ = π492 75 10000

92 dx 10000 75 02 = 2401 π (x-30000) |-75

2401兀 (92 dx 10000 75 130-730u) 2401 π | 92- 75-(-75)3 92923 30000 957814.8668