Question

Question #9d0af

Answer 1

If it were a whole cylinder, the volume would be:

`V = pir^2h`

But we have only part of a cylinder.

If we knew `theta`, we could multiply by it and divide by `2pi`

`V = pir^2htheta/(2pi)`

`pi/pi` cancels:

`V = r^2htheta/2`

Move the `1/2` to the front:

`V = 1/2r^2htheta" [1]"`

We know that the length of the arc is the product of angle (in radians) and the radius:

`L_"arc" = thetar`

Solve for `theta`:

`theta = L_"arc"/r" [2]"`

Substitute equation [2] into equation [1]:

`V = 1/2r^2hL_"arc"/r`

One of the r factors cancel:

`V = 1/2rhL_"arc"`

He have all of these values, `r = 6"mm", h=26.5"mm", and L_"arc" =14"mm"`:

`V = 1/2(6"mm")(26.5"mm")(14"mm")`

`V = 1113"mm"^3`

I hope that this is your answer.

Answer 2

`"The volume of this shape" = 3153mm^3`

Explanation:

Firstly, we find the volume of the triangular prism:

`V = (bh)/2 xx h`

`V= (14 xx 6)/2 xx 26.5`

`42^2 xx 26.5 = 1113mm^3`

Then find the volume of half the cylinder:

`V= (πr^2h)/(2)`

`V=( 7^2 xx pi xx 26.5)/2`

`V = 2039.67903mm^3`

Now we need to add the two volumes that we calculated to get the total volume of the two shapes.

`2039.67903 + 1113 = 3152.67093mm^3`

`color(blue)(= 3153mm^3`