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2 years ago

Given a sphere with a diameter of 4 inches, what is the volume of the sphere. write it out.

Mathematics

1 answer:

Art [367]2 years ago

4 0

Answer:

around 33.51

Step-by-step explanation:

Hello! :)

Let’s start with the basics:

How to Find the Volume of a Sphere:

Formula: V= 4/3 $\pi$ r^3, which means the volume is 4/3 times the approximation of pi (3.14 or 22/7) time the radius with an exponent of 3.

Now that we know how to find the volume of a sphere, let’s solve the actual problem :D

The diameter is 4. We have to find the radius to find a volume of a sphere.

The radius is the diameter divided by 2; that makes our radius, 2.

So, V= 4/3 $\pi$ (2)^3
Let’s solve the exponent first. 2^3= 2(2)(2) which is 8.

Now, you can either solve 4/3 times 8 first, or 4/3 times pi. I’m going to solve 4/3 times 8 to make it a little bit easier.

4/3 times 8= 32/3 which is around 10.7 (10.6667).

Now, let’s do 10.7 times pi. (I’ll be using 3.14 as the approximation of pi.)

10.7 x 3.14= 33.598 (actual answer using 10.6667 is 33.51).

And there you go! I hope this helps, let me know if you have any questions/I did anything wrong. Good luck! :D

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Could someone help me rnnn?

GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola: $y=3x^2-4$

Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

(where (h, k) is the vertex and $a$ is some constant)

Substitute point (0, -4) into the equation:

$\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}$

Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$

Substitute point (1, -1) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}$

Equate to find h:

$\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}$

Substitute found value of h into one of the equations to find a:

$\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}$

Substitute found values of h and a to find k:

$\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}$

Therefore, the equation of the parabola in vertex form is:

$\implies y=3(x-0)^2-4=3x^2-4$

So the vertex of the parabola is (0, -4)

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