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ioda
3 years ago
13

Which expression can be used to find the volume of the sphere? diameter is 10 inches

Mathematics
2 answers:
8090 [49]3 years ago
5 0

Answer:

\large\boxed{V=\dfrac{4}{3}\pi R^3=\dfrac{D^3}{6}\pi}\\\\\boxed{V=\dfrac{500\pi}{3}\ in^3\approx523.33\ in^3}

Step-by-step explanation:

\text{The formula of a volume of a sphere:}\\\\V=\dfrac{4}{3}\pi R^3\\\\R-radius\\\\\text{A diameter}\ D=2R\Rightarrow R=\dfrac{D}{2}.\\\\\text{Therefore}\\\\V=\dfrac{4}{3}\pi\left(\dfrac{D}{2}\right)^3=\dfrac{4}{3}\pi\left(\dfrac{D^3}{8}\right)=\dfrac{D^3}{6}\pi

\text{We have the dimater}\ D=10in.\ \text{Substitute:}\\\\V=\dfrac{10^3}{6}\pi=\dfrac{1000}{6}\pi=\dfrac{500\pi}{3}\ in^3

RSB [31]3 years ago
4 0

For this case we have that by definition, the volume of a sphere is given by:

V = \frac {4} {3} \pi * r ^ 3

Where:

r: It is the radius of the sphere

We are told as data that the diameter of the sphere is 10in, so the radius is 5in:

V = \frac {4} {3} \pi * 5 ^ 3\\V = \frac {4} {3} \pi * 125\\V = \frac {500} {3} \pi\\V = 523.33in ^ 3

Answer:

V = \frac {4} {3} \pi * 5 ^ 3\\V = \frac {4} {3} \pi * 125\\V = \frac {500} {3} \pi

Any of the three given expressions can be used to find the volume of the sphere.

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Four squared equals 16

Step-by-step explanation:

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1 year ago
Express it in slope-intercept form.
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6 0
3 years ago
1: n/-3 - 8 &lt; 17<br> 2: n/-2 + 11 &gt; 17
cupoosta [38]

Answer:

1: n > -75

2: n < -12

Step-by-step explanation:

1: n/-3 - 8 < 17

n/-3 (- 8 + 8) < 17 + 8

n/-3 < 25

n/-3(-3) < 25(-3)

n < -75

n > -75 (switch symbol when you divide or multiply by a negative number)

2: n/-2 + 11 > 17

n/-2 (+ 11 - 11) > 17 - 11

n/-2 > 6

n/-2(-2) > 6(-2)

n > -12

n < -12 (switch symbol when you divide or multiply by a negative number)

7 0
2 years ago
Taylor and Nora go to the movie theater and purchase refreshments for their friends. Taylor spends a total of $69.00 on 6 drinks
fgiga [73]

Answer:

The system if equation that can be used to derive this are

6x + 4y = 69 AND

12x + y = 96

The price of a drink is $7.5

Step-by-step explanation:

The question here says that Taylor and Nora went to the movie theater and purchase refreshments for their friends. Taylor spends a total of $69.00 on 6 drinks and 4 bags of popcorn Nora spends a total of $96.00 on 12 drinks and bag of popcorn.And we are now told to write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations,we should determine and state the price of a drink, to the nearest cent .

Now, Let's assume that the price of a drink is "X" and that of a bag of popcorn to be Y

The first person made a purchase which led to the equation

6x + 4y = 69______ equation 1

And the second person also made a purchase that lead to the equation

12x + y = 96_____ equation 2

We make y the subject of the formula in equation 2 and apply it in 1

Y = 96 - 12x

Now apply the above in equation 1

6x + 4y = 69

6x + 4(96 - 12x)= 69

6x + 384 - 48x = 69

42x = 384 - 69

X = 315/42

X = 7.5

Substitute x= 7.5 in equation 2

12x + y = 96

12(7.5) + y = 96

90 + y = 96

Y = 6

Therefore, the price of a drink is $7.5

4 0
3 years ago
Read 2 more answers
X^3+3x^2y+3xy^2+y^3<br> ————————————<br> X^3+y^3
Hoochie [10]
To factor this fraction, you have be be aware of two special factoring formula:
a^3<span> + </span>b^3<span> = (</span>a<span> + </span>b)(a^2<span> – </span>ab<span> + </span>b^2<span>)

</span><span>(a+b)³ = a³ + 3a²b + 3ab² + b³

You can see the top part in this case is (x+y)^3, and the bottom (denominator) can be factor into (x+y)(x^2-xy+y^2)
we can cancel (x+y), so what we have left is (x+y)^2/(x^2-xy+y^2)
or (x^2+2xy+y^2)/(x^2-xy+y^2)
</span>
7 0
3 years ago
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