Question

Volume of a cylinder. Can I get some help please? I've been trying for almost an hour and I can't find a good answer. Thanks a lot!

Answer 1

`V = pir^3 + 7pir^2`

`log_81 3 =1/4`

Explanation:

You will need to start with the formula for the volume of a cylinder.

`Vol = "area of the base (which is a circle)" xx "Height of cylinder"`

`V = pir^2 xx h" "larr` there are two variables. `r and h`

You have been told that the height is `7` in. more than the radius

`r = r " " and " "h = (r+7)`

So now you can rewrite the formula using only one variable, `r`.

`V = pir^2xx (r+7)`

`V = pir^3 + 7pir^2" "larr` if you multiply out the bracket.

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`log_81 3` is asking " how do you make `81` into `3`?

(logs are just a way of writing indices, so do this by using powers and roots)

It will help to know that `3^4 = 81`

`3^4 =81`

`3 = root4 (81) = 81^(1/4)`

`:. log_81 3 = 1/4`

Using index form:

`log_81 3 = x" "rArr" " 81^x= 3`

Solving as an exponential equation:

`(3^4)^x = 3^1" "larr` the bases are equal

`:. 4x =1" "larr` the indices are equal

`x =1/4`