Question

A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 5 inches. The height of the cone is 15 inches.

Use π = 3.14.

What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.

Answer 1

I could really use some help on this..

Answer 2

im gonna run through it with you

Answer 3

ok thank you so much!!

Answer 4

Volume of a cylinder:

V=πr2h

V=(3.14)(4)2(5)

What's 4 * 4?

Answer 5

16 right?

Answer 6

Yes, and what's 3.14 * 16 * 5?

Answer 7

251.2 I think.

Answer 8

yes

Answer 9

Volume of a cone:

V=13πr2h

V=13(3.14)(4)2(15)

What's 1/3 * 3.14 * 16 * 15?

Answer 10

.....oh I get it! thank you so much!

Answer 11

so u got the rest

Answer 12

I think so but could you tell me if im right.

Answer 13

yea

Answer 14

oh I think I messed it up could you tell me what I should do now?

Answer 15

the volume of a cone is ONE THIRD the volume of a cylinder.

Answer 16

relationship is that they're the same

Answer 17

ok so I think i get it. so for the question I just put down the work and then explain the different of a cone and cylinder.

Answer 18

explain the relationship between them

Answer 19

Volume of a cone is 1/3 the volume of a cylinder with the same base.

Cone = V= 1/3 Bh where the B = the base area and h is the height

Area of a circle = πr² (if the diameter is 8 the radius of this circle is 4)
A = π4² = π16 usually notated as 16π (numerical coefficients come first)

V= 1/3 x 16 x 18
V= 6 x 16 (I took 1/3 of 18 which is 6)
V of the cone = 96 π in³
Volume of a cylinder is = Bh or in this case 16π x 18 = 288π
Comparing the two you can see that the cylinder is 3 x the volume of the cone or the cone is 1/3 the volume of the cylinder.

Answer 20

ok I did it thanks. do you think you could help me with 3 more in a different box?

Answer 21

sure if i can