Volume of cylinder,hemisphere and involves trignometry

[tidal mist]

Could somebody please help me solve this question step by step SIMPLIFIED because otherwise i might not understand where one value came from.Thanks.

[cedar mica]

Work out the vertical height, use trig and find the hypotenuse, which is the length of the rod

[tidal mist]

How do I do the vertical height?

Could u explain it in more detail please

[cedar mica]

I haven't learnt volume of cylinder wtv

What's the equation for it?

[cerulean current]

πr²h

[cedar mica]

V = πr²h

22.1 = π(1.5)²h

22.1 = 2.25π x h
22.1/2.25π = h
h = 3.12651043763

Length opposite the angle is 3.12651043763. Use sin(71) = 3.12651043763/h and rearrange to get h.
sin(71) x h = 3.12651043763, so h = 3.12651043763/sin(71). Insert that into your calculator and you'll find the length of the rod.

@tidal mist ^

It's correct if v = πr²h is the correct formula

[cedar mica]

@prime compass ^

[prime compass]

That’s the volume for the cylinder

You need to remember to add on the volume of the hemisphere

[cedar mica]

how would you work that out?

is there a formula for it?

[prime compass]

Uhh there is but I don’t remember it

I have a feeling it’s just half the volume of a sphere

[cedar mica]

oh ok ty

[prime compass]

Yeh it is just half the volume of a sphere

$\frac{2\pi r^3}{3}$

[placid flicker]

clarence

[cedar mica]

I see thanks

[tidal mist]

Alright thank you,I’ll try

[cedar mica]

take into consideration what clarence said above

[tidal mist]

Will do thanks

[cedar mica]

np

[tidal mist]

I add the volume of the hemisphere to the cylinder and then do the trigonometry right?

[cedar mica]

yes

[tidal mist]

I got 10.78254216

It says it isn’t the correct answer

[tidal mist]

Can u help me please

[cedar mica]

vol of hemisphere is half volume of a sphere

work out the volume of a sphere using its equation

/2

and add it onto the vol of the cyclinder

[cedar mica]

then use these steps but with the correct volume

[tidal mist]

I did