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
kramer
3 years ago
8

A cone of radius 10 cm and height 16 cm is divided into two parts by a plane through the midpoint of its

Mathematics
1 answer:
bazaltina [42]3 years ago
7 0

Answer:

The ratio of their volumes (the top to bottom half) is 1/7

Step-by-step explanation:

The given parameters are;

The radius, r, of the cone = 10 cm

The height of the cone = 16 cm

The point at which the cone is divided = The midpoint of the its axis and parallel to its base

The ratio of the of the volume of the two parts is given as follows;

The volume, V of the entire cone = 1/3 × Base area (π·r²) × Height, h

Therefore;

V = 1/3 × π × 10² × 16 =1600·π/3 =  1675.52 cm³

The height at which the cone is divided = 16/2 = 8 cm

The height, h₁ of the uppermost divided cone = 8 cm

The ratio of the radius to the height of the cone = 10/16 = 5/8

The radius r₁, of the uppermost divided cone = The height of the uppermost divided cone × The ratio of the radius to the height of the cone

∴ r₁ = 8 × 5/8 = 5 cm

The volume, V₁, of the uppermost divided cone = 1/3 × (π·r₁²) × h₁

∴ V₁ = 1/3 × π × 5² × 8 = 200·π/3 = 209.44 cm³

Which gives;

The volume of the lower cone, V₂ =  V - V₁

V₂ =  1675.52 cm³ - 209.44 cm³ = 1400·π/3 = 1466.1 cm³

The ratio of their volumes V₁ : V₂ = V₁/V₂ = (200·π/3)/(1400·π/3) = 209.44/1466.1 = 1/7.

You might be interested in
What is 49/16 as mixed number
Georgia [21]
3 1/16

Divide 49 by 16 and then multiply the whole number by 16 to find out the 1/16
4 0
3 years ago
Read 2 more answers
If b=5 what is b to the power of 5
Sonja [21]

Answer: 5^5 = 3125

Step-by-step explanation:

To the power of mostly means multiplying it by itself the number of times giving so for your problem it is 5 times itself 5 times so 5*5*5*5*5 = 3125

5 0
2 years ago
Read 2 more answers
Find the principal square root of 14.
Anika [276]
Sqrt14 = 3.74 (2dp)

The principal root is always the positive.
5 0
2 years ago
Which expressions are equivalent to -f-5(2f-3)
gizmo_the_mogwai [7]

Answer:

-11f +15

Step-by-step explanation:

-f-5(2f-3)

Distribute

-f -10f +15

Combine like terms

-11f +15

3 0
3 years ago
Read 2 more answers
The Bengals football team scored 2 touchdowns for 6 points each, one extra point, and 3 field goals for 3 points each. The Raven
Yanka [14]

bangles scored 22 pts but don't know how much the ravens scored


4 0
3 years ago
Other questions:
  • PLZ HELP ME PLZ PLZ! Find the product.
    9·2 answers
  • Math question please help <br> If you get this right I will mark you as a brainliest
    5·1 answer
  • i need help with 3 (along with 3a-c) i am confused on what to do with the numbers that are in degrees...
    13·2 answers
  • Which of the following represents the characteristics of the graph of x ≥ -9?
    12·2 answers
  • Help I need help with this plz help
    14·1 answer
  • 4c &lt; 28 <br><br> Solve the inequality
    9·1 answer
  • In right angle ABC, a = 12, b = 9, and c = 15. Find tan ∠B
    15·1 answer
  • What is the quotient of the following division problem?
    9·1 answer
  • a. A bag contains 7 b l u e marbles, 10 g r e e n marbles, and 5 r e d marbles. If a marble is drawn from the bag, replaced, and
    11·1 answer
  • Back to school is coming and laura is
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!