Question

Janine made a cylindrical vase in which the sum of the lateral area and area of one base was about 3000 square centimeters. The vase had a height of 50 centimeters. Find the radius of the vase. Explain the method you would use to find the radius.

Answer 1

3000= (h* l) + pi * r^2
l=2*pi*r
3000= (h * 2*pi*r) + pi * r^2

3000 = (50 * 2*pi*r)+ pi * r^2
3000=50pir + pir^2

what do I do after this?

Answer 2

\[\Large A_{lateral}+A_{bottom}=3000 \\ \\ \Large 2\pi rh+\pi r^2=3000 \\ \\ \text{When} ~~h=50, r=?\]

Answer 3

Yep you're in the right track, you need to factor that, use quadratic equation

Answer 4

\[\pi r^2+50\pi r-3000=0 \\ \\ r=\frac{-50\pi \pm \sqrt{2500\pi ^2-4(\pi)(-3000)}}{2\pi}\]

Answer 5

How do i simplify that?

Answer 6

\[r=\frac{-50\pi \pm \sqrt{2500\pi^2+12000\pi}}{2\pi} \\ \\ r=-25 \pm \frac{\sqrt{2500\pi^2+12000\pi}}{2\pi} \\ \\ r=-25 \pm \frac{\sqrt{2500(3.142)^2+12000(3.142)}}{2(3.142)} \\ \\ r=-25 \pm 39.75 \\ \\ r=-25+39.75, ~~~r=-25-39.75 \\ \\ r=14.74, ~~~r=-64.75\]

Answer 7

But since 'r' cannot be negative, then it is r=14.74cm

Answer 8

Thank you !

Answer 9

Wait hold on
Your answer from 3000 = (50 * 2*pi*r)+ pi * r^2
Should get you 3000 = (100*pi*r)+ pi * r^2

Answer 10

\[\pi r^2+100 \pi r=3000\]

Answer 11

\[r=\frac{-100\pi \pm \sqrt{10000\pi ^2-4(\pi)(-3000)}}{2\pi} \\ \\ r=8.77cm\]

Answer 12

How do you get so many different answers for "r"?

Answer 13

The 14.74 is a mistake,
Your answer from 3000 = (50 * 2*pi*r)+ pi * r^2
Should get you 3000 = (100*pi*r)+ pi * r^2

Then that should give you r=8.77cm

Answer 14

Alright thank you!

Answer 15

would the units be squared?

Answer 16

no because it is length, not area or volume

Answer 17

It's just cm

Answer 18

thanks again.