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
vagabundo [1.1K]
1 year ago
7

In order for this ratio of volumes to be true, what measurements would have to be equal in all 3 solids?

Mathematics
1 answer:
Neporo4naja [7]1 year ago
4 0

The measurements of the figures that should be equal in order for the ratio of volumes between the volumes of the cone, sphere, and cylinder of 1:2:3 to be true is; The radius and the height

<h3>What is a ratio?</h3>

A ratio is a comparison between the magnitudes or measurements of items, expressing the number of times one item in the ratio is contained within another item in the ratio.

The formula for the volume of a cone, V_p is, V_p = (1/3)·π·r₁²·h₁

The formula for the volume of a sphere, V_s, is V_s = (4/3)·π·r₂³

The formula for the volume of a cylinder, V_c, is V_c = π·r₃²·h₃

The ratio of the volumes in the question is 1:2:3

Therefore; The volume of the sphere is twice the volume of the cone, and the volume of the cylinder is three times the volume of the cone, which indicates;

(4/3)·π·r₂³ = 2 × (1/3)·π·r₁²·h₁...(1)

π·r₃²·h₃ = 3 × (1/3)·π·r₁²·h₁...(2)

Equation (1) indicates that we have;

(4/3)·π·r₂³ = 2 × (1/3)·π·r₁²·h₁

Where, h₁ = 2·r₂, we get;

(4/3)·π·r₂³ = 2 × (1/3)·π·r₁²·(2·r₂) = (4/3)·π·r₁²·r₂

Therefore; r₁ = r₂, and the diameter of the sphere is equal to the height of the cone

The radius of the cone is equal to the radius of the sphere

Equation (2) indicates;

π·r₃²·h₃ = 3 × (1/3)·π·r₁²·h₁ = π·r₁²·h₁

Therefore;

r₃²·h₃ = r₁²·h₁

r₃ = r₁

h₃ = h₁

The radius of the cone = The radius of the cylinder

The height of the cone = The height of the cylinder

  • The ratio of the volumes, 1 : 2 : 3 is true when the measurements of the radius and the height are equal for all three solids.

Learn more about the volume of regular solids here:

brainly.com/question/15316195

#SPJ1

You might be interested in
jasmine has taken an online boating safety course and is now completing her end of course exam.As she answers each question, the
Alexus [3.1K]
20% of 16 which is. 10%=1.6 and another that would = 3.12
6 0
3 years ago
Eleven of 20 students in Mr. Gonzalez ‘s science class are attending the field trip. What percent best represents the portion of
antoniya [11.8K]

Answer:

%55

Step-by-step explanation:

divide both values by 2, multiply by 10 to give you a percentage


3 0
3 years ago
In a particular region, for families with a combined income of $75,000 or more, 15% of these families have no children, 35% of t
SCORPION-xisa [38]

Answer:

The probability distribution for x:"number of children per family for this income group" is:

\text{P(x=0)}=0.15\\\\\text{P(x=1)}=0.35\\\\\text{P(x=2)}=0.45\\\\\text{P(x=3)}=0.05\\\\

Step-by-step explanation:

With the information given we have the relative frequencies of each category.

We know:

\text{P(x=0)}=0.15\\\\\text{P(x=1)}=0.35\\\\\text{P(x=2)}=0.45\\\\\text{P(x=3)}=0.05\\\\

7 0
3 years ago
harry owes the bank money.To replay his debt,he paid $150 back to the bank each month . After 10 months, his remaining debt was
Maksim231197 [3]
Answer: 8400 $

Explanation:
His original debt: money paid for 10 months + remaining debt
Assume X is his original debt
Then X= 10 • 150 + 6900
X= 1500+6900=8400$
8 0
3 years ago
When using the given diagram to determine the area of the gray polygon by decomposition, which statements are correct?:
Klio2033 [76]
It’s B)area b=27x3nqkqkoqlqlqq
7 0
3 years ago
Read 2 more answers
Other questions:
  • Buddy is about 6inches long. It took three point five rows of stiches to make 0.5 inches in length for buddy's sweater. How many
    12·2 answers
  • What 3 even numbers add up to 54
    12·2 answers
  • PLEASE HELP. What are some facts about the number 99 that would make you like it as your favorite number? Thank you in advance.
    10·1 answer
  • Given that (- 2, 7) is on the graph of f(x) , find the corresponding point for the function f(x + 4).
    12·1 answer
  • Simplificar A=4x2-6x2+7x2-20x2+19x2
    11·1 answer
  • What is 4/5 +3/2+5/3
    8·1 answer
  • Help!!!!!!!!!!!!!!!!!!!!!
    12·2 answers
  • What is the missing angle measurement in the polygon shown below?
    12·2 answers
  • Which of the following is the solution to the equation 25(z + 4) = 125?
    11·1 answer
  • PLEASE HELP 20 POINTS AND WILL GIVE BRAINLIEST
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!