Finding the volume of a cone with fractions

[cosmikoi]

there's a question on the GED practice test for finding the volume of a cone:

I started with the equation for the volume: SA = πrs + πr², and first I tried to get the radius. I took 2 3/4 and turned it to an improper fraction which is 11/4. I need to divide this in half because right now its the diameter, but I don't know how to divide a fraction in half, and the explanation for the answer they gave doesn't explain how:

how did they divide it in half? and once i do plug 11/4 into the equation, how would i square the fraction?
thanks in advance

 

[MarkFL]

The diameter of the base in inches is:

[MATH]\frac{11}{4}[/MATH]
And so the radius is half of that (double the denominator)

[MATH]\frac{11}{8}[/MATH]
Now, the formula for the volume is:

[MATH]V=\frac{\pi}{3}r^2h[/MATH]
Plug in the values for \(r\) and \(h\) (noting that cubic inches will be the resulting unit):

[MATH]V=\frac{\pi}{3}\left(\frac{11}{8}\right)^2(4)=\frac{\pi}{3}\left(\frac{121}{64}\right)(4)=\frac{\pi}{3}\left(\frac{121}{16}\right)=\frac{121\pi}{48}\approx7.9[/MATH]

 

[Harry_the_cat]

there's a question on the GED practice test for finding the volume of a cone:
View attachment 12948
I started with the equation for the volume: SA = πrs + πr², and first I tried to get the radius. I took 2 3/4 and turned it to an improper fraction which is 11/4. I need to divide this in half because right now its the diameter, but I don't know how to divide a fraction in half, and the explanation for the answer they gave doesn't explain how:
View attachment 12949
how did they divide it in half? and once i do plug 11/4 into the equation, how would i square the fraction?
thanks in advance

You said: "I started with the equation for the volume: SA = πrs + πr², and first …".
That's where you went wrong. That is the formula for surface area - you even have "SA = …"