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3 years ago

The formula for the volume sphere is V=4/3pie r^3 what is the formula solved for r?

Mathematics

2 answers:

oksian1 [2.3K]3 years ago

3 0

Answer:

$r = \sqrt[3]{\frac{3V}{4 \pi}}$

Step-by-step explanation:

From the formula of volume of a sphere we have to isolate "r" on one side of the equation i.e. we have to make "r" the subject of the equation.

$V=\frac{4}{3} \pi r^{3}\\\\ \text{Multiplying both sides by 3/4 we get}\\\\\frac{3V}{4} = \pi r^{3}\\\\ \text{Dividing both sides by } \pi \\\\ \frac{3V}{4 \pi} = r^{3}\\\\\text{Takeing cube root of both sides}\\\\\sqrt[3]{\frac{3V}{4 \pi}} = r$

Therefore:

$r = \sqrt[3]{\frac{3V}{4 \pi}}$

juin [17]3 years ago

3 0

Answer:

The formula for radius of sphere is r = ∛(3V/4π)

r = (3V/4π)¹/³

Step-by-step explanation:

It is given formula for volume of sphere.

Volume of sphere = 4/3 πr³

Where r is the radius of sphere

To find the radius r of sphere 

Volume V = 4/3 πr³

r³ = 3V/4π

r = ∛(3V/4π)

Therefore formula for radius of sphere is r = ∛(3V/4π)

r = (3V/4π)¹/³

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2 years ago

A test has 50 questions. each right answer is worth 2 points; each wrong answer deducts 0.5 points; blank answers are not counte

mestny [16]

ANSWER: There are 2 blank answers

EXPLANATION

Let

The number of right answers be ‘r’

The number of wrong answers be ‘w’

The number of blank answers be ‘b’

r + w + b = 50

This means r + w ≤ 50

Then we know,

Right answers = 2 marks

Wrong answers = -0.5 mark

Blank Answers = 0 marks

2r – 0.5w = 88.5

2r = 88.5 + 0.5w … (Equation I)

Since the score as .5, we know that there is at least one wrong answer, and the number of wrong answers is an odd number.

Since the score is 88.5, and each right answer gives 2 marks

There are at more than 44 (i.e. 88/2) right answers

Since r + w ≤ 50, and possible values of w are odd numbers

If r = 45, Possible values of w are 1, 3, and 5

If r = 46, Possible values of w are 1, 3

If r = 47, Possible values of w are 1, 3

If r = 48, The only possible value of w is 1

If r = 49,The only possible value of w is 1

Since 2r = 88.5 + 0.5w (Equation I)

We test for possible values:

If r = 45

2r = 88.5 + 0.5w

2(45) = 88.5 + 0.5w

90 = 88.5 + 0.5w

0.5w = 90 – 88.5

0.5w = 1.5

w = 3

So,

If there are 45 right answers

There are 3 wrong answers

r + w + b = 50

45 + 3 + b = 50

48 + b = 50

b = 50 – 48

b = 2

Then, there are 2 blank answers.

If r = 46

2r = 88.5 + 0.5w

2(46) = 88.5 + 0.5w

92 = 88.5 + 0.5w

0.5w = 92 – 88.5

0.5w = 3.5

w = 7

So,

If there are 46 right answers

There are 7 wrong answers

We know that r + w ≤ 50

46 + 7 = 53

So 46 and higher numbers are not possible solutions.

The only possible solution is:

There are 45 right answers

There are 3 wrong answers

There are 2 blank answers

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