1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
pickupchik [31]
3 years ago
7

A.) The formula for the volume of a sphere is given below and the relationship between the radius r and the diameter d is r=d/2.

Find the EXACT volume of the sphere in terms of the diameter d. Be sure to fully simplify the expression.
B.) What is the EXACT volume of the sphere when the diameter is 2/3 centimeter?
Mathematics
1 answer:
Tasya [4]3 years ago
8 0

Answer:

\displaystyle V=\frac{4}{81}\cdot \pi\ cm^3

Step-by-step explanation:

<u>The Volume of a Sphere </u>

The volume of a sphere of radius r is given by:

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

A. )

If the diameter of the sphere is d, the radius is r=d/2. Substituting:

\displaystyle V=\frac{4}{3}\cdot \pi\cdot \left (\frac{d}{2}  \right )^3

Operating

\displaystyle V=\frac{4}{3}\cdot \pi\cdot \frac{d^3}{8}

Simplifying

\displaystyle V=\frac{1}{6}\cdot \pi\cdot d^3

B.)

The diameter of the sphere is 2/3 cm, thus the volume is:

\displaystyle V=\frac{1}{6}\cdot \pi\cdot \left (\frac{2}{3}  \right )^3

Operating:

\displaystyle V=\frac{1}{6}\cdot \pi\cdot \frac{8}{27}

\displaystyle V=\frac{8}{27}\frac{1}{6}\cdot \pi

\boxed{\displaystyle V=\frac{4}{81}\cdot \pi\ cm^3}

You might be interested in
A large emerald with a mass of 378.24 grams was recently discovered in a mine. If the density of the emerald is 2.76 grams over
stepan [7]

Answer:

  • 137.04 cm³

Step-by-step explanation:

  • Mass = Density*Volume
  • V = m/d
  • V = 378.24/2.76 = 137.04 cm³ (rounded)
5 0
3 years ago
Read 2 more answers
From the quadratic equation 3x² + X - 5 = 0, find alpha square plus beta square​
timama [110]

Answer:

  α² +β² = 3 4/9

Step-by-step explanation:

Assuming α and β are solutions to the equation, it can be factored as ...

  (x -α)(x -β) = 0

Expanding this, we get ...

  x² -(α +β)x +αβ = 0

Dividing the original equation by 3, we find ...

  x² +(1/3)x -5/3 ≡ x² -(α+β)x +αβ   ⇒   (α+β) = -1/3, αβ = -5/3

We know that the square (α+β)² can be expanded to ...

  (α +β)² = α² +β² +2αβ

  α² +β² = (α +β)² -2αβ . . . . . . subtract 2αβ

Substituting the values for (α+β) and αβ, we find the desired expression is ...

  α² +β² = (-1/3)² -2(-5/3) = 1/9 +10/3 = 31/9

  α² +β² = 3 4/9

4 0
2 years ago
3. Find the difference between the two expressions.<br> 1x - 5y)-1(x + 2y)
Fittoniya [83]

Answer:

-7y

Step-by-step explanation:

Our equation is:

\left(1x-5y\right)-1\left(x+2y\right)

First we dritribute

Now we have, x-5y-x-2y

Combine light terms

and we get -7y

5 0
3 years ago
What is the area of the trapezoid?
Ostrovityanka [42]
I hope this helps you

6 0
3 years ago
Plz helpp
den301095 [7]

Answer:

Addition Property of Equality If AB = CD then AB + BC = BC +CD

Subtraction Property of Equality If AB + BC = BC + CD then AB = CD

Multiplication Property of Equality If m∢A = 90 then 2(m∢A) = 180

Division Property of Equaliity If 2(m∢B) = 180 then m∢B = 90

Substitution Property If m∢A + m∢B =180 and m∢B then m∢A + 90 =180

Distributive Property AB + AB = 2AB

Reflexive Property m∢B = m∢B

Symmetric Property If AB + BC = AC then AC = AB + BC

Transitive Property If AB ≅ BC and BC ≅ CD then AB ≅ CD

Segment Addition Postulate If C is between B and D, then BC + CD = BD

Angle Addition Postulate If D is a point in the interior of ∢ABC then m∢ABD + m∢DBC = m∢ABC

Linear Pair Postulate If two angles form a linear pair, then they are supplementary

Definition of Right Angle If ∢B is a right angle then m∢B = 90

Definition of Midpoint If P is the midpoint of segment AB then AP =PB

Definition of Segment Bisector If k intersects segment AB at M the Midpoint then k bisects segment AB

Definition of Perpendicular Lines If two lines are ⊥ they form right angles

Definition of Congruent Segments If AB = CD then segment AB ≅ segment CD

Definition of Congruent Angles If ∡A ≅∡ B then m∡A=m∡B

Definition of Angle Bisector If ray AB bisects ∡CAD then∡ CAB ≅ ∡ BAD

Definition of Complementary Angles If ∡ Z and ∡Y are complementary m∡Z +m∡Y =90

Definition of Supplementary Angles If ∡ S and ∡T are supplementary m∡S +m∡T = 180

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • Need help with 2 3 and 4, show work if possible
    12·1 answer
  • Which symbol makes the sentence true?
    5·1 answer
  • In 1998, Cathy's age is equal to the sum of the four digits in the year of her birthday, then how old was Cathy in 1998?
    8·1 answer
  • Two angles are supplementary. One angle is 80 degrees. What is the value of the other angle? please hurry
    11·2 answers
  • mrs thomson Is buying two types of gift cards to give as prizes to employees at a company meeting. Do you buy restaurant gift ca
    7·1 answer
  • In 1 minute, Alex can type 44 words. While working on a project, Alex types from 10:00 AM until 1 AM, He takes a break from 1 0:
    12·1 answer
  • Can someone help me! it would mean the world! and tysm! &lt;3
    5·1 answer
  • suppose you plunk $5000 into a one-year certificate of deposit (CD) that pays simple interest at 3% per annum. The interest you
    9·2 answers
  • Mathematics of inequality
    11·1 answer
  • Instructions: Interpret the function given in the context of the real-world situation described to answer the question.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!