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
kirill115 [55]
3 years ago
14

A metallic sphere is immersed in water in a cylindrical container causing a rise in the level of water by 7.5cm if the cylinder

has a base radius of 7cm find the radius of the sphere to 2 decimal places
Mathematics
1 answer:
SVETLANKA909090 [29]3 years ago
3 0

Answer:

6.51 cm

Step-by-step explanation:

Since the sphere causes the water level in the cylindrical container to rise and thus increase by its own volume, the volume of the sphere is V = 4πr³/3 where r = radius of sphere. The volume rise of the container is thus    V' = πR²h where R = radius of base of cylinder = 7 cm and h = height of water level = 7.5 cm.

Since V = V',

4πr³/3 = πR²h

dividing through by π, we have

4r³/3 = R²h

multiplying both sides by 3/4, we have

r³ = 3R²h/4

taking cube-root of both sides, we have

r = ∛(3R²h/4)

Substituting the values of the variables into the equation, we have

r = ∛(3(7 cm)² × 7.5 cm/4)

r = ∛(3 × 49 cm² × 7.5 cm/4)

r = ∛(1102.5cm³/4)

r = ∛(275.625 cm³)

r = 6.508 cm

r ≅ 6.51 cm to 2 decimal places

You might be interested in
Examine this right triangle,
Ipatiy [6.2K]
A^2 + 16^2 = 20^2
(Third one)
6 0
3 years ago
What is the height of the triangle? 12 units 24 units 36 units 72 units.
konstantin123 [22]

Height of the triangle is the altitude of the triangle and which is drawn perpendicular from the vertex of the triangle to the opposite side. The height of the tringle is 24 units. Hence option 2 is the correct option.

<h3>Given information-</h3>

The triangle for the given problem is shown in the image below.

Form the figure the length of the each side is 16 \sqrt{3} units.

As all the sides are equal thus the \Delta MNO is a equilateral triangle in which the height of the divides the triangle into two equal part of the length 8\sqrt{3} at point <em>R.</em>

<h3>Height of the triangle-</h3>

Height of the triangle is the altitude of the triangle and which is drawn perpendicular from the vertex of the triangle to the opposite side.

Now in the  \Delta MRN, the length of the hypotenuse is 16 \sqrt{3} units and the length of the base is 8\sqrt{3} units. Let <em>h </em>is the height of the triangle thus by the Pythagoras theorem,

(16\sqrt{3})^2 =(8\sqrt{3})^2+h^2

Solve for <em>h,</em>

<em />

<em />\begin{aligned}h^2 &=(16\sqrt{3})^2 -(8\sqrt{3})^2\\h^2 &=16\times16\times3 -8\times8\times3\\h^2 &=576\\h &=\sqrt{576}\\h &=24\\\end<em />

<em />

Thus the height of the tringle is 24 units. Hence option 2 is the correct option.

Learn more about the equilateral triangle here;

brainly.com/question/4268382

5 0
2 years ago
(4y+3)-(y-2) find the sum or difference. answer quickly, please!
Paladinen [302]

Answer:

0

Step-by-step explanation:

4 0
3 years ago
In the number 2145857, how does the digit 5 in the thousands place compare to the digit 5 in the tens place?
fgiga [73]
It is 1,000 bigger than the one in the tens place. 5,000 compared to 50 
7 0
4 years ago
Find the quotient: 8,441 ÷ 21 = ________. a. 400 r 12 b. 400 r 20 c. 401 r 12 d. 400 r 20
Irina18 [472]

Answer:

Step-by-step explanation:

8441/21= 401 r 20

8 0
3 years ago
Other questions:
  • Hey! I would really love it if someone could help me
    5·1 answer
  • G squared multiplied by G squared
    9·1 answer
  • Substitute<br>x+y =200<br>9.5x+27y=4000​
    12·1 answer
  • This data represents the number of oil changes completed each day last week at Jeff's Auto Center. 19, 16, 24, 12, 16, 21, 18 Wh
    6·1 answer
  • Solve the following equations 19=7+y
    11·2 answers
  • X = A 21.6 B 12.9 C 9.1
    6·2 answers
  • Someone tell me where everyone is going right please !!
    13·2 answers
  • 3. Six Flags charges $16 for a refillable
    9·1 answer
  • Which is true about the triangle in the diagram?
    9·1 answer
  • Can you guys help me with this please the question is on the screen shot
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!