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3 years ago

A sphere has the volume given. Find its surface area to the nearest whole number.

1 answer:

6 0

Volume of the sphere = 900 cubic inch
Then
4/3 pi (r)^3 = 900
pi (r)^3 = (900 * 3)/4
= 675
r^3 = 675/pi
= 675/3.14
r^3 = 214.97
r = 6
Then
Surface area of the sphere = 4 pi (r)^2
= 4 * 3.14 * (6)^2
= 4 * 3.14 * 36
= 452.16
= 452
The surface area of the sphere given in the question is 452 square inches.

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Find+the+positive+value+for+α+if+the+radius+of+the+circle+3x^2+3y-6αx+12y-3α=0+is+4

Alik [6]

Answer:

$\alpha=3$

Step-by-step explanation:

<u>Equation of a Circle</u>

A circle of radius r and centered on the point (h,k) can be expressed by the equation

$(x-h)^2+(y-k)^2=r^2$

We are given the equation of a circle as

$3x^2+3y^2-6\alpha x+12y-3\alpha=0$

Note we have corrected it by adding the square to the y. Simplify by 3

$x^2+y^2-2\alpha x+4y-\alpha=0$

Complete squares and rearrange:

$x^2-2\alpha x+y^2+4y=\alpha$

$x^2-2\alpha x+\alpha^2+y^2+4y+4=\alpha+\alpha^2+4$

$(x-\alpha)^2+(y+2)^2=r^2$

We can see that, if r=4, then

$\alpha+\alpha^2+4=16$

Or, equivalently

$\alpha^2+\alpha-12=0$

There are two solutions for $\alpha$ :

$\alpha=-4,\ \alpha=3$

Keeping the positive solution, as required:

$\boxed{\alpha=3}$

8 0

3 years ago

PLEASE HELP I HAVE NO IDEA WHAT IM DOING!!!

algol13

Answer: 28.26

Step-by-step explanation:

What your looking for is called the annulus (or the difference of two concentric circles). You can find the annulus by subtracting the area of the inner circle from the area of the outer circle. Volume of a circle= πr²

You are given the diameter in these problems, so you need radius.

For the first circle (8 in one) :

8/2=4 r=4

A=3.14(4)²

A=50.24

For the second one (10 in one) :

10/2=5 r=5

A=3.14(5)²

A=78.5

To find the measure of the annulus, you subtract those numbers, getting 28.26

8 0

3 years ago