Question

Consider the volume of the region shown below, which shows a right circular cone with top radius 3 cm and height 10 cm. We have used the notation Dy for \Delta y

Answer 1

I have the same problem here with a slight change in the given values:

radius is 2 & height of 6 indicates the bounding line is y = 3 x---> x = y / 3.... 

thus the [ π radius ² thickness ] yields π (y² / 9 ) dy , y in [ 0 , 6 ] for the volume... 

a Riemann sum is then : y_i = 0 + i [ 6 / n ] = 6 i / n , i = 1,2,3...n and do a right side sum 

π Σ { i = 1,2,3..n } [ 36 i² / 9 n² ] [ 6 / n ]

I hope my guide has come to your help. God bless and have a nice day ahead!

Answer 2

The volume of the figure will be 94.2cm^3

Assuming we are solving for volume of a cone with the limited information given

Data given

• radius = 3cm
• height = 10cm
• volume of cone = ?

Volume of Cone

The formula of volume of a cone is given as

$v=\frac{1}{3}\pi r^2h$

Let's substitute the values and solve for the volume

$v = \frac{1}{3}\pi r^h\\v = \frac{1}{3}*\pi * 3^2 * 10\\v= \frac{1}{3}*3.14*9*10\\ v = 94.2cm^3$

The volume of the figure will be 94.2cm^3

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