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.

Question

yanasidlinskiy · Answer

This is what I have:
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anonymous · Answer

the lateral área is like área of a rectangle with hight=50 and
 length equal to circle length = 2$\pi$r
are of base is área of circle = $\pi r^2$, so:
adding this two you need to get around 3000:
(2$\pi r\cdot $50)+$\pi r^2$=3000
this a quadratic equation. Solve it for r

mathmate · Answer

Area of the base (assuming a vase is open at the top)
$$=\pi r^2\ cm^2$$
Lateral Area
$$= 2\pi rh\ cm^2$$
$$= 100\pi r\ cm^2$$

If the total surface area is 3000 cm2, then
$$\pi r^2 + 100\pi r = 3000$$
Form the following quadratic equation and solve for r:
$$\pi r^2 + 100\pi r - 3000 = 0$$
to give r=8.77 cm or -108...
Reject the illogical value.