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2 years ago

If given the volume of a cylinder, how would you find the volume of a sphere that has the same radius measure.

Mathematics

1 answer:

Digiron [165]2 years ago

7 0

Answer:

The radius of a sphere hides inside its absolute roundness. A sphere's radius is the length from the sphere's center to any point on its surface. The radius is an identifying trait, and from it other measurements of the sphere can be calculated, including its circumference, surface area and volume. The formula to determine the volume of a sphere is 4/3π multiplied by r, the radius, cubed, where π, or pi, is a non terminating and non repeating mathematical constant commonly rounded off to 3.1416. Since we know the volume, we can plug in the other numbers to solve for the radius, r.

Multiply the volume by 3. For example, suppose the volume of the sphere is 100 cubic units. Multiplying that amount by 3 equals 300.
Divide this figure by 4π. In this example, dividing 300 by 4π gives a quotient of 23.873.
Calculate the cube root of that number. For this example, the cube root of 23.873 equals 2.879. The radius is 2.879 units.

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Mekhanik [1.2K]

Answer:

5.51 meters

Step-by-step explanation:

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3 years ago

A triangle is formed from the points L(-3, 6), N(3, 2) and P(1, -8). Find the equation of the following lines:

Dima020 [189]

Answer:

Part A) $y=\frac{3}{4}x-\frac{1}{4}$

Part B) $y=\frac{2}{7}x-\frac{5}{7}$

Part C) $y=\frac{2}{7}x+\frac{8}{7}$

see the attached figure to better understand the problem

Step-by-step explanation:

we have

points L(-3, 6), N(3, 2) and P(1, -8)

Part A) Find the equation of the median from N

we Know that

The median passes through point N to midpoint segment LP

step 1

Find the midpoint segment LP

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

we have

L(-3, 6) and P(1, -8)

substitute the values

$M(\frac{-3+1}{2},\frac{6-8}{2})$

$M(-1,-1)$

step 2

Find the slope of the segment NM

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

N(3, 2) and M(-1,-1)

substitute the values

$m=\frac{-1-2}{-1-3}$

$m=\frac{-3}{-4}$

$m=\frac{3}{4}$

step 3

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=\frac{3}{4}$

$point\ N(3, 2)$

substitute

$y-2=\frac{3}{4}(x-3)$

step 4

Convert to slope intercept form

Isolate the variable y

$y-2=\frac{3}{4}x-\frac{9}{4}$

$y=\frac{3}{4}x-\frac{9}{4}+2$

$y=\frac{3}{4}x-\frac{1}{4}$

Part B) Find the equation of the right bisector of LP

we Know that

The right bisector is perpendicular to LP and passes through midpoint segment LP

step 1

Find the midpoint segment LP

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

we have

L(-3, 6) and P(1, -8)

substitute the values

$M(\frac{-3+1}{2},\frac{6-8}{2})$

$M(-1,-1)$

step 2

Find the slope of the segment LP

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

L(-3, 6) and P(1, -8)

substitute the values

$m=\frac{-8-6}{1+3}$

$m=\frac{-14}{4}$

$m=-\frac{14}{4}$

$m=-\frac{7}{2}$

step 3

Find the slope of the perpendicular line to segment LP

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

$m_1*m_2=-1$

we have

$m_1=-\frac{7}{2}$

$m_2=\frac{2}{7}$

step 4

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=\frac{2}{7}$

$point\ M(-1,-1)$ ----> midpoint LP

substitute

$y+1=\frac{2}{7}(x+1)$

step 5

Convert to slope intercept form

Isolate the variable y

$y+1=\frac{2}{7}x+\frac{2}{7}$

$y=\frac{2}{7}x+\frac{2}{7}-1$

$y=\frac{2}{7}x-\frac{5}{7}$

Part C) Find the equation of the altitude from N

we Know that

The altitude is perpendicular to LP and passes through point N

step 1

Find the slope of the segment LP

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

L(-3, 6) and P(1, -8)

substitute the values

$m=\frac{-8-6}{1+3}$

$m=\frac{-14}{4}$

$m=-\frac{14}{4}$

$m=-\frac{7}{2}$

step 2

Find the slope of the perpendicular line to segment LP

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

$m_1*m_2=-1$

we have

$m_1=-\frac{7}{2}$

$m_2=\frac{2}{7}$

step 3

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=\frac{2}{7}$

$point\ N(3,2)$

substitute

$y-2=\frac{2}{7}(x-3)$

step 4

Convert to slope intercept form

Isolate the variable y

$y-2=\frac{2}{7}x-\frac{6}{7}$

$y=\frac{2}{7}x-\frac{6}{7}+2$

$y=\frac{2}{7}x+\frac{8}{7}$

7 0

3 years ago

Find the average value of the function over the given interval and all values of x in the interval for which the function equals

MrRissso [65]

The average value of $f(x)=4x^3-3x^2$ over [-1, 3] is

$\displaystyle\frac1{3-(-1)}\int_{-1}^3(4x^3-3x^2)\,\mathrm dx=\frac14\left(x^4-x^3\right)\bigg|_{-1}^3=\frac{(3^4-3^3)-(1+1)}4=\boxed{13}$

8 0

2 years ago

14, 8, 17, 21, x, 11,<br> 3, 13; range: 20

MakcuM [25]

Answer:

x = 1

Step-by-step explanation:

When you subtract the smallest number from the biggest number, the answer is called the range. Here the largest number is 21. The smallest is 3. Then the range should be 18. But since it's 20. This mean that x is 1. Because 21 - 1 will equal 20, making 20 the range. So the correct answer is 1.

6 0

3 years ago

Given f(x)=px+q and f^3(x)=8x-7<br>find value of p and q<br><br>

Zielflug [23.3K]

Answer:answer is 17

Step-by-step explanation:

8(3) - 7

24-7

6 0

2 years ago