A sphere has a diameter of 14 units. What is the volume of the sphere in cubic units? If a cylinder has the same radius as the sphere and a height of 14 units, what is the volume of the cylinder? Use 3.14 for π.
A.
The volume of the sphere is about 1,077.02 cubic units, and the
volume of the cylinder is about 718.01 cubic units.
B.
The volume of the sphere is about 1,436.03 cubic units, and the
volume of the cylinder is about 2,154.04 cubic units.
C.
The volume of the sphere is about 1,436.03 cubic units, and the
volume of the cylinder is about 957.35 cubic units.
D.
The volume of the sphere is about 1,077.02 cubic units, and the
volume of the cylinder is about 1,615.53 cubic units.

Question

A sphere has a diameter of 14 units. What is the volume of the sphere in cubic units? If a cylinder has the same radius as the sphere and a height of 14 units, what is the volume of the cylinder? Use 3.14 for π.
A. 
The volume of the sphere is about 1,077.02 cubic units, and the
volume of the cylinder is about 718.01 cubic units.
B. 
The volume of the sphere is about 1,436.03 cubic units, and the
volume of the cylinder is about 2,154.04 cubic units.
C. 
The volume of the sphere is about 1,436.03 cubic units, and the
volume of the cylinder is about 957.35 cubic units.
D. 
The volume of the sphere is about 1,077.02 cubic units, and the
volume of the cylinder is about 1,615.53 cubic units.

kittybasil · Answer

The formula for the volume of a sphere is (source: here)$$V=\frac{4}{3}\pi r^3$$However, you are asked to use "3.14" instead of the $\pi$ symbol. So your actual formula for this problem should then be$$\therefore V=\frac{4}{3}(3.14)r^3$$

aidenj · Answer

im so confused

kittybasil · Answer

The radius $r$ is half the diameter $d$, and you are given $d=14$ (units) for the sphere. Thus, the radius should be $r=\frac{d}{2}=\frac{14}{2}=7$ Sphere radius should be 7 units. We're working with the sphere if you're not sure which part I'm referring to

kittybasil · Answer

All good so far?

aidenj · Answer

not rlly but ill try

aidenj · Answer

@snowflake0531

kittybasil · Answer

Okay, where are you lost? I can try re-explaining

aidenj · Answer

by everything

aidenj · Answer

wait so 3.14 and 14 do we multiply ro soemthing

rabo102 · Answer

yall miss a need help with this

kittybasil · Answer

Alright, let's start over then.
Your question is asking for two things:
1) the volume of a sphere with diameter 14 units.
2) the volume of a cylinder with the same diameter as the sphere (14 units) and a height of 14 units.

With me so far?

aidenj · Answer

yes

rabo102 · Answer

yeah

kittybasil · Answer

Okay, so we were working on part one there, finding the volume of the sphere. I will quote what I said earlier:

kittybasil wrote:

The formula for the volume of a sphere is (source: here)$$V=\frac{4}{3}\pi r^3$$However, you are asked to use "3.14" instead of the $\pi$ symbol. So your actual formula for this problem should then be$$\therefore V=\frac{4}{3}(3.14)r^3$$

The radius $r$ is half the diameter $d$, and you are given $d=14$ (units) for the sphere. Thus, the radius should be $r=\frac{d}{2}=\frac{14}{2}=7$ Sphere radius should be 7 units.

Make sense so far? If it doesn't, just ask me to re-explain anything.

aidenj · Answer

yes im with u

rabo102 · Answer

im confused

kittybasil · Answer

... I just typed up a whole response and the site just deleted it. Hold on rq

aidenj · Answer

let me guess again

kittybasil · Answer

every time I tab out to check something the site deletes my response :|

kittybasil · Answer

So sorry. But basically you put 7 instead of $r$ in the next step, and I was going to say that $$7^3=7\cdot7\cdot7=49\cdot7=343$$so your next step after that should be$$V=\frac{4}{3}(3.14)(343)$$

aidenj · Answer

ok can u give me a way to the answer to hurry this up forgive me tho

kittybasil · Answer

Nah I got you, no worries. But you understand so far? before I move on

aidenj · Answer

yes

kittybasil · Answer

Okay, so our next step is to simplify this fraction-multiplication thing.$$V=\frac{4}{3}(3.14)(343)=\frac{4\cdot343\cdot3.14}{3}=\frac{1372\cdot3.14}{3}=\frac{4308.08}{3}\approx1,436.0267$$(I had to cut that down because the calculator answer was WAY longer than that)
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With me so far?

aidenj · Answer

b

aidenj · Answer

or c

aidenj · Answer

keep going

kittybasil · Answer

I'm going to assume you understand my last comment...

aidenj · Answer

yes

aidenj · Answer

i rounded and everything so yeah

kittybasil · Answer

Okay, so now we move on to step 2, finding the volume of a cylinder with these dimensions:
DIAMETER 14 units (aka RADIUS 7 units as we established earlier)
HEIGHT 14 units
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The formula for cylindrical volume is:$$V_{cyl}=\pi r^2h$$However, as we discussed earlier, the problem wants you to replace $\pi$ with 3.14, so:$$\therefore V_{cyl}=(3.14)r^2h$$

kittybasil · Answer

Minor post-it note: I forgot to mention that all values for "volume" should have SQUARE units. Since your units are literally called "units" that would make it $u^3$ in shorthand form.
<hr class="bbcode_rule" />
Back to cylinder volume, $r=7$ and $h=14$ so:$$V_{cyl}=(3.14)(7)^2(14)$$Now we simplify.

But first... got everything so far?

aidenj · Answer

yeah

kittybasil · Answer

Okay, let's keep going then -$$V_{cyl}=3.14\cdot49\cdot14=3.14\cdot686=2,154.04\text{ u}^3$$ And that should be your cylinder's volume.

Combining this with your sphere volume, $V_{sphere}=1,436.0267\text{ u}^3$... which choice should be correct then?

Quick recap: volume of a sphere is $V_{sphere}=\frac{4}{3}\pi r^3$ and volume of a cylinder is $V_{cylinder}=\pi r^2h$

aidenj · Answer

B thanks so much kitty

kittybasil · Answer

Note: if you can't see the red stuff I said "which choice should be correct then?" source for cylinder volume: here

btw I go by Kitt, but no problem 😀 Cheers! • Kitt

aidenj · Answer

tys kitt cya