Can somebody help me with this math problem?

Question

A cylinder has a height of 10 and a surface area of 78pi. Find the radius and volume of this cylinder. (pi=3.14)

I totally forgot how to solve this. Does this require the quadraic formula?

Answer 1

The area of a cylinder requires two parts:

C×h = (2πr)h = 20πr for the lateral area

(that's circumference × height)

2πr² for the two circular ends.

(twice the area of a circle)

The equation becomes:

20πr + 2πr² = 78π

This does involve the quadratic formula. But you can simplify it out quite a bit, by canceling common factors. You should NOT be dealing with πs in your quadratic formula!!! What a mess!

10r + r² = 39

r² + 10r - 39 = 0

And you don't need the quadratic formula, because you can factor this equation:

(r - 3)(r + 13) = 0

r = 3 or r = -13

We ignore the negative values (r is a radius, it can't be negative) and arrive at r=3 as the final value.

The volume is the area of the base times the height:

A = bh = πr²h = 10π(3²) = 90π

which is approximately 3.14×90 = 282.6

Answer 2

The surface of one end of the cylinder would be pi r^2.
The sides would have a surface of 10 * 2 pi r.

Thus the equation is
2 pi r^2 + 20 pi r = 78pi
(A cylinder has *two* ends.)

r^2 + 10 r - 39 = 0;
(r + 13)(r -3) = 0

Thus r can either be -13 or 3. A negative radius would be nonsensical, so the radius of the cylinder would be 3.

The volume is 10 pi r^2, which simplifies to 90 pi, or about 282.74 Since pi is only specified to 3 significant places, we should round that to an even 283.

Answer 3

As Paul Ding pointed out up above, a cylinder has 2 ends.

Volume = pi*r*r*h (pi r-squared height)
Surface Area = (height * circumference of the circle) + (Area of the circle * 2)
Circumference = 2*pi*r
Area = pi*r*r (pi r-squared)

Substitute in for surface area:

78*pi = 20*pi*r + 2*pi*r*r

divide both sides by 2*pi

39 = 10*r + r*r

move everything to one side

r*r + 10*r - 39 = 0

Use the quadratic formulat to solve

r = [ -10 +/- squareroot(10*10 - (4*1*-39))]/(2*1)
r = [-10 +/- squareroot(100 + 156)]/2
r = (-10 +/- squareroot(256))/2
r = (-10 +/- 16)/2
r = 3 or -13
r = 3

Volume = 10*3*3*pi = 90*pi = approximately 282.6


Everyone saying that r = 3.9 is WRONG because they aren't accounting for the surface of the ends of the cylinder. You need both the surface area around the height of the cylinder (height * circumference) AND the area of the bases (2 * area of your circle).

Answer 4

2(pi)(r squared)+(10)(2)(pi)r=78 pi
2 x surface area of circle face + 10 (which is the height) x (2x pi x r) which is the circumference

divide both sides by pi to eliminate it...
2(r squared) + 20 r = 78
divide both sides by 2...
r squared +10 r = 39
r squared +10r - 39 = 0
(r+13)(r-3)=0

r can only be 3


volume = pi x (r squared) x height

height is 10...so figure out from there...

Answer 5

So have I, but I suspect the surface area formula is 2 * pi * r * h where is a constant, so if you know the area and h, you can find out r. Then the volume is pi * r^2 * h.

Answer 6

We know that the surface area of a cylinder is 2pi*r*h
therefore,
2*pi*r*10=78 pi
r=78/(2*10)=3.9 units
Hence Volume
=pi*r^2*h
=3.14*3.9*3.9*10
=477.6 cubic units

Answer 7

14 is 30% of what numer? write as 14 = .3X, X is what you want. Divide the two factors via .3, or 14/.3 = X = 40 six.667 what's two% of 40? you want .02*40 = 0.8 sammy sosa had 193 hits, his batting familiar became 0.320 (32%) this is the whole of at-bats (32%) what share at-bats did he have? this suggests 193/ B = .32, the place B is the selection at-bat. go multiply. 193 = .32 B, divide via .32 or B = 193/.32 = 603.one hundred twenty five or 603.

Answer 8

The surface area of a cylinder is the circumference of the circle that is its cross-section by it's height, or pi * d * h.

78 * pi / 10 = 7.8 * pi = pi * d. d = 7.8

r then = 3.9.

Volume = pi * r^2 * h = 3.9^2 * 10 * pi = 15.21 * 10 * pi = 152.1 * pi

Answer 9

surface area = 2*pi*r*h
(r-radius, h-height)
78pi=2pi*r*10
r=78pi/20pi
r=3.9

Volume = pi*r^2*h
=3.14*3.9^2*10
=477.594

Answer 10

surface area = 2pir^2 + 2pirh
= 2pir(r+h)

so 36 = r(r+h)

if h = 10 then
36 = r^2 + 10r
0 = r^2 + 10r - 36
r = [-10 +- sqrt(100+144)]/2
r = -5 +- sqrt(61)