Question

medal for whoever can walk me through this!!!
A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of π.)

Answer 1

First find the volume of both the cylinder and cone.

Answer 2

Do you have a graph to see the position of the cone inside the cylinder?

Answer 3

v=pi(r^2)h is this right?

Answer 4

3.14*25*16 = 1256
would this be right for the cylinder?

Answer 5

help???

Answer 6

AravindG is right, you have to find the volume of the cone and substract it from the volume of the cylinder.
Vol(Cyl)=BaseArea*Height=(PI*R^2)*h
Vol(Con)=(PI*R^2*h)/3

Volume of air inside the cylinder and outside the cone = Vol(Cyl)-Vol(Con)
Vol(Air) = (PI*R^2*h)-(PI*R^2*h)/3
Vol(Air) = (3.14*5^2*16)-(3.14*4^2*12)/3 [cm^3]
Vol(Air) = ((3.14*5^2*16)-(3.14*4^2*12)/3) [cm^3]
Vol(Air) = (1256 - 200.96) [cm^3]
Vol(Air) = 1055.04 [cm^3]

Answer 7

@fgancarelli that look sick :/
did I get the volume for the cone right?
when you find the volume of a cone do you always multipy by 1/3

Answer 8

v=1/3 pi(r^2)h
1/3*3.14*16*12=200.96
1055.04cm

Answer 9

Yes, if you google "Cone volume" you will find that there is a special formula to calculate it, and that formula is:
Volume of a cone with radius "R" and heigh "h" = (PI*R^2*h)/3
In wikipedia and many other sites they show you where does this formula come from

Answer 10

1055.04cm^3
I just saw now you posted the answer. I was so distracted by all those numbers. thanks for helping.

Answer 11

Here is a video from a great teacher explaining why does the volume of a cone equals that formula: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-volume/v/volume-cone-example

Answer 12

thanks!

Answer 13

@fgiancarelli In this question the slanted cube would still have the same volume yes?
the volume would be the same? 1000 cubic feet


The cube in the image has a volume of 1,000 cubic feet. The other solid has the same base and height as the cube, but the length of each of its slanted sides is 2 units longer than the height. What is the volume of the tilted solid?