Question

Jenny is building a model of a futuristic spaceship for her art class. For the engine, she plans to cut a cone in half and combining it with a cylinder as shown in the diagram below.

Using the diagram, which of the following answer choices is closest to the volume, in cubic inches, of Jenny's spaceship engine?

Answer 1

@SolomonZelman

Answer 2

I can see the cylinder, but I don't get what is protruding on the sides from the cylinder?

Answer 3

First lets find the volume of the cylinder.

Find the area of the circle \(\Huge\color{blue}{ \sf A= πr^2 }\)
(your diameter is 4, so radius is going to be half of that. r=?)


can you find the area of the circle ?

Answer 4

the area for the circle will be 12.56 right?

Answer 5

yeah, you got it right !

Answer 6

No there is 14 inches of those (12.56-inch) areas in the cylinder. Right?

Answer 7

14 times, not 14 inches.

Answer 8

so whats the area

Answer 9

You found the area of the circle. it's 12.56 inch.

now multiply that times height of the cylinder to get cylinder's volume

the volume of the cylinder = ?

Answer 10

=175.84

Answer 11

yes right again.

Answer 12

what are these pieces on the sides of your cylinder?

Answer 13

those are the two pieces of cone that were cut

Answer 14

I see.

I forgot the formula for the volume of the cone.

Answer 15

\(\Huge\color{blue}{ \sf V= \frac{1}{3}bh }\)

Answer 16

so a half of a cone would be

\(\Huge\color{blue}{ \sf \frac{1}{6}bh }\) correct ?

Answer 17

its 1/3πr(to the second power)h

Answer 18

for the volume of a right circular cone

Answer 19

Oh, my bad. OK

Answer 20

\(\Huge\color{blue}{ \sf \frac{1}{3}πr^2h }\) THIS ?

Answer 21

yes

Answer 22

so what do you know about the cone?

Answer 23

(the diagram)

Answer 24

what i do know is that each piece that was cut is 1 inch

Answer 25

Hold on, on your diag. is 6 a diagonal of cone or is it the height of the cone ?

Answer 26

its the height

Answer 27

and 1 represents what ?

Answer 28

i guess the length?

Answer 29

the length? the radius you mean?

or the length of the "1/2-piece" of the cone.

Answer 30

plug in 1 for radius and 6 for height into

\(\Huge\color{blue}{ \sf \frac{1}{3} πr^2h }\)

h=6
r=1
π=3.14

the volume of half of cone = ?

Answer 31

=6.28

Answer 32

Yes, correct !

Answer 33

and 2 of those half cones are added going to be equal to ?

Answer 34

=12.56

Answer 35

and + the volume of the cylinder, (which was 175.84 ) ?

Answer 36

188.4

Answer 37

YES ! There you go !

Answer 38

so thats the answer

Answer 39

omg thank you so much do u think u can help me with 2 more or no?

Answer 40

@SolomonZelman

Answer 41

I am abt to go offline, I am finishing up. Sorry.

it's 11:28 in my time zone

Answer 42

11:28 pm

Answer 43

ok : (