Write a rational number between root2 and root3

Given: R=2m

mr_godi [17]

Answer:

$V = \frac{2L\sqrt{3}}{3} \pi}$

$A = 4\pi + \sqrt{3L^{2} + 16}$

Step-by-step explanation:

Figure of cone is missing. See attachment

Given

Radius, R = 2m

Let L = KL=LM=KM

Required:

Volume, V and Surface Area, A

Calculating Volume

Volume is calculated using the following formula

$V = \frac{1}{3} \pi R^{2} H$

Where R is the radius of the cone and H is the height

First, we need to determine the height of the cone

The height is represented by length OL

It is given that KL=LM=KM in triangle KLM

This means that this triangle is an equilateral triangle

where OM = OK = $\frac{1}{2} KL$

OK = $\frac{1}{2}L$

Applying pythagoras theorem in triangle LOM,

|LM|² = |OL|² + |OM|²

By substitution

L² = H² + ( $\frac{1}{2}L$ )²

H² = L² - $\frac{1}{4}L$ ²

H² = L² (1 - $\frac{1}{4}$ )

H² = L² $\frac{3}{4}$

H² = $\frac{3L^{2} }{4}$

Take square root of bot sides

$H = \sqrt{\frac{3L^{2} }{4}}$

$H = \frac{L\sqrt{3}}{2}$

Recall that $V = \frac{1}{3} \pi R^{2} H$

$V = \frac{1}{3} \pi 2^{2} * \frac{L\sqrt{3}}{2}$

$V = \frac{1}{3} \pi * 4} * \frac{L\sqrt{3}}{2}$

$V = \frac{1}{3} \pi} * {2L\sqrt{3}}$

$V = \frac{2L\sqrt{3}}{3} \pi}$

in terms of $\pi$ an d L where L = KL = LM = KM

Calculating Surface Area

Surface Area is calculated using the following formula

$H = \frac{L\sqrt{3}}{4}$

$A=\pi r(r+\sqrt{h^{2} +r^{2} } )$

$A=\pi * 2(2+\sqrt{((\frac{L\sqrt{3}}{2})^{2} +2^{2} } )$ )

$A=\pi * 2(2+\sqrt{{\frac{3L^{2}}{4} } + 4 }$ )

$A=\pi * 2(2+\sqrt{{\frac{3L^{2}+16}{4} } })$

$A=2\pi(2+\sqrt{{\frac{3L^{2}+16}{4} } })$

$A = 2\pi (2 + \frac{\sqrt{3L^{2} + 16}}{\sqrt{4}} )$

$A = 2\pi (2 + \frac{\sqrt{3L^{2} + 16}}{2} )$

$A = 2\pi (2 + {\frac{1}{2} \sqrt{3L^{2} + 16})$

$A = 4\pi + \sqrt{3L^{2} + 16}$

6 0

3 years ago

Find the slope of the line that passes through the pair of points

love history [14]

Answer:

$\frac{5,805}{2812}$

Step-by-step explanation:

To find the slope from two points you can use the following formula:

$m = \frac{y -y_{1} }{x -x_{1} }$

Now substitute the two sets of points $(\frac{7}{20}, \frac{5}{19} ) and (\frac{5}{9}, \frac{11}{16})$

Substitute the values like this:

$y = \frac{5}{19}, y_{1} = \frac{11}{16}, x = \frac{7}{20}$ and $x_{1} =\frac{5}{9}$

Now you will need to simplify the following expression:

$m = \frac{\frac{5}{19} -\frac{11}{16} }{\frac{7}{20}-\frac{5}{9} }$

Make sure that denominators are the same before substracting:

$m = \frac{\frac{-129}{304} }{\frac{-37}{180} }$

when you divide with a fractional number you only need to flip the second fraction over (find its reciprocal). Then just multiply:

$m = (\frac{-129}{304} })({\frac{-180}{37} } ) = \frac{5805}{2812}$

5 0

3 years ago

In cell B8 created a formula without using a function that multiplies the value in cell B7 by the value in cell B6 and then adds

nata0808 [166]

4. In cell-B8, create a formula without using a function that multiplies the value.in.cell.B7. by the value-in-cell-B6-andthen adds-the-value in B7..Update.the-cell-reference to cell: B6, from a relative reference to a mixed-reference by making an absolute-reference to row.6..Copy-the-formula-from-cell-B8-to-the-range-B9:B11-and-then-copy-the-formulas. from the range-B8:B11-to-the-range-C8:H11.1 13. SALO extend the list of years to the range A15:A17.1 In-cell-B13, create-a formula without a function using absolute references that subtracts the values of cells.B5 and B7.from.cell-B6 and then multiplies the result.by.cell-B8. Copy the formula-from-cell-B13 to the range C13:H13.1 In-cell-B14, create-a formula without using a function that adds.1.to the value-in-cell B12 and then multiplies the result by the value-in-cell-B13Update-the-referenceto-cell B12, from a relative-reference to a mixed-reference by making an absolute reference to row.12. Copy the formula-from-cell-B14-to-the-range-B15:B17 and then copy the formulas.from-the-range-B14:B17 to the range-C14H17.1

4 0

3 years ago

When constructing parallel lines , how can you verify the lines constructed are parallel

tamaranim1 [39]

Answer:

compare the distance between the lines at one point to the distance between the lines at another point

Step-by-step explanation:

You can construct perpendiculars at different points and compare the distance between the lines at those perpendiculars. The distance between parallel lines is the same everywhere.

8 0

3 years ago

Read 2 more answers

If you reflect triangle MOV across the x-axis, what is the coordinate of O in the image?

Zina [86]

Hi,

The answer you are looking for is 2. (-4,2)

Have a great day & remember to mark brainliest if I helped :)

4 0

3 years ago

Read 2 more answers

Write a rational number between root2 and root3​

Write a rational number between root2 and root3