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
The pyramid shown has a square base that is 12 centimeters on each side. The slant height is 18 centimeters. What is the surface
iogann1982 [59]
A = 576 cm2 hope that helps ;)<span>
</span>
8 0
3 years ago
Read 2 more answers
A 4-inch long ribbon is cut into pieces. If the length of each piece is 12of an inch, how many pieces are cut?
vekshin1

Answer:

48 pieces are cut.

Step-by-step explanation:

1/12 of an inch means that one inch would be 12 pieces. Since there are 4 pieces it would be 12x4= 48 pieces.

5 0
3 years ago
What’s the answer my phone calculator isn’t working
zubka84 [21]

Answer:

4.33

Step-by-step explanation:

If you don't have the cube root function in your calculator, u can chose a choice instead and cube the value.

9x9 is already 81, hence 9x9x9 > 81

27 x 27 Is definitely more than 81

Hence the only reasonable answer is 4.33

5 0
3 years ago
What algebraic expression is a polynomial
nata0808 [166]

Answer:In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. An example of a polynomial of a single indeterminate, x, is x2 − 4x + 7.

Step-by-step explanation:

Hope this helps

stay safe

plz give brainiest if this helped

4 0
3 years ago
Sue uses the expression 8x3000+ 8x200+ 8 x 9 to help solve a multiplication problem what is sues multiplication problem
Iteru [2.4K]

we know that

the expression (8x3000+ 8x200+ 8 x 9) is equal to

8*3,000+ 8*200+ 8 * 9 =8*(3,000+200+9)\\  =8*(3,209)\\  = 25,672

therefore

<u>the answer is</u>

Sue's multiplication problem is to find the product of 8 times 3,209 in expanded form


6 0
3 years ago
Read 2 more answers
Other questions:
  • IM BEGGING YOU PLEASE ANSWER EASY MATH QUESTIOON!!!!
    11·2 answers
  • Can Someone please help me?
    12·1 answer
  • Is √17 rational irrational an integer a whole number or a natural number.
    15·1 answer
  • number has 6 digits smallest digit is 0.01 largest digit is 8,000 digit in the tens is 2 less than digit on the hundreds the sum
    11·1 answer
  • I need the answer for p
    12·1 answer
  • Sue's Fruit Stand sells 20 different types of fruits. The table below shows the numbers of fruits that have certain percentages
    9·1 answer
  • What is (x+3,y) a translation,rotation,reflection, or dilation
    12·1 answer
  • What is the slope of 2y + 8x = 20
    5·1 answer
  • Translate the following word sentence into a numerical expression: When you square five times a number, you get three more than
    6·1 answer
  • Part B Isabella's mother sells the peas and gets $3 for each square foot. So, multiply your answer from Part A by 3 to calculate
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!