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AnnZ [28]
3 years ago
5

Can someone leave their work in the answer section or at least the solution

Mathematics
1 answer:
kenny6666 [7]3 years ago
5 0
Find 6% of 3,500 and 4% of 4,000 then subtract the two
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A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21m. what is the volume of the sphere.​
Goshia [24]

Answer:

The volume of the sphere is 14m³

Step-by-step explanation:

Given

Volume of the cylinder = 21m^3

Required

Volume of the sphere

Given that the volume of the cylinder is 21, the first step is to solve for the radius of the cylinder;

<em>Using the volume formula of a cylinder</em>

The formula goes thus

V = \pi r^2h

Substitute 21 for V; this gives

21 = \pi r^2h

Divide both sides by h

\frac{21}{h} = \frac{\pi r^2h}{h}

\frac{21}{h} = \pi r^2

The next step is to solve for the volume of the sphere using the following formula;

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

Divide both sides by r

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

Expand Expression

\frac{V}{r} = \frac{4}{3}\pi r^2

Substitute \frac{21}{h} = \pi r^2

\frac{V}{r} = \frac{4}{3} * \frac{21}{h}

\frac{V}{r} = \frac{84}{3h}

\frac{V}{r} = \frac{28}{h}

Multiply both sided by r

r * \frac{V}{r} = \frac{28}{h} * r

V = \frac{28r}{h} ------ equation 1

From the question, we were given that the height of the cylinder and the sphere have equal value;

This implies that the height of the cylinder equals the diameter of the sphere. In other words

h = D , where D represents diameter of the sphere

Recall that D = 2r

So, h = D = 2r

h = 2r

Substitute 2r for h in equation 1

V = \frac{28r}{2r}

V = \frac{28}{2}

V = 14

Hence, the volume of the sphere is 14m³

4 0
3 years ago
Read 2 more answers
G(x)= 3/4x+6<br> What is the value of g(12)?
gizmo_the_mogwai [7]

Answer:

G(12) = 15

Step-by-step explanation:

When doing g(x) equations, all you do is substitute the value inside the parentheses to x in the equation.

So you get 3/4(12) + 6.

Then simplify to get g(12) = 15

4 0
3 years ago
What is the simplified form of 30 times x to the sixth power over 14 times y to the fifth power times the fraction 7 times y-squ
Sonbull [250]
If we convert the given in its mathematical form, we have,

                      (30x⁶/14y⁵)(7y²/6x⁴)
It can be observed that the numerator of the first and the denominator of the second have a common factor of 6x⁴. Also, the denominator of the first and the numerator of the second expression have a common factor of 7y².

                      ((6x⁴)(5x²)/(7y²)(2y³))(7y²/6x⁴)

Cancellation of the common terms will give us an answer of,
  
                               <em>5x²/2y³

</em>
<em />Therefore, the simplified version of the involved operation is 5x²/2y³. <em>
</em>
6 0
3 years ago
Please help !!
xxMikexx [17]
I hope this helps you

5 0
3 years ago
Read 2 more answers
Which set of numbers is correctly ordered from greatest to least?
Nina [5.8K]

Answer:

It's D.

Step-by-step explanation:

Convert each number to decimal format.

It is option D , if we convert as above we get

7.36799, 7.36666.., 7.363636.., 7.33333..

4 0
3 years ago
Read 2 more answers
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