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 has a height of 50 centimeters. Find the radius of the vase. Explain the method you would use to find the radius

Answer 1

SA = 2r(pi) + (pi)r^2
3000 = 2r(pi) + (pi)r^2
(pi)r^2 + 2(pi)r - 3000 = 0
using quadratic formula:
r = [-2(pi) +/- SQR((2(pi))^2 - 4(pi)(-3000))]/2(pi)
r = [-2(pi) +/- SQR((2(pi))^2 + 12,000(pi))/2(pi)
using pi = 3.14:
r = [-6.28 +/- SQR(39.4 + 37,680)/6.28
r = [-6.28 +/- 194]/6.28
r = 29.9 or -31.9
using the positive root:
r = 29.9cm
check:
3000 = 2(29.9)(3.14) + (3.14)(29.9^2)
3000 = 187.8 + 2807.2
3000 = 2995

Answer 2

I got this far but i didn't put the height in can someone help please

Answer 3

SA = 2r(pi)h + (pi)r^2

Answer 4

and where would that go in the equation?

Answer 5

(pi)r^2 + 2(pi)hr - 3000 = 0

Answer 6

so at the very end?

Answer 7

r = [-2(pi)h +/- SQR((2(pi)b)^2 - 4(pi)(-3000))]/2(pi)
r = [-2(pi)*50 +/- SQR((2(pi)*50)^2 - 4(pi)(-3000))]/2(pi)

Answer 8

Can you write the whole equation that i wrote and write in the parts that i forgot

Answer 9

\[r = \frac{-100\pi \pm \sqrt{(100\pi^2) - 4\pi(-3000)}}{2\pi}\]
\[r = \frac{-100\pi \pm \sqrt{10000\pi^2 + 12000\pi}}{2\pi}\]

Answer 10

do you understand what I am asking?

Answer 11

not really

Answer 12

\[r = -50\pm\sqrt{\frac{10000\pi^2}{4\pi^2} + \frac{12000\pi}{4\pi^2}}\]

Answer 13

\[r = -50\pm\sqrt{2500 + \frac{3000}{\pi}}\]

Answer 14

I dont have the height yet, i missed it in my problem that I figured out and I just need the height and you to show me where it goes thats it

Answer 15

well i have put h i n the right places and you see h =50 so the quadratic formula will come out differently

Answer 16

oh ok well where would it go in my problem

Answer 17

the lateral surface area of the cylinder is a rectangle

one side is the circumference of the circle, the other side in the height of the cylinder,

A = 2πr • h

Answer 18

so the sum of the lateral area and area of one base

SA = 2πr•h + πr^2

Answer 19

ok thank u