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
Gnesinka [82]
3 years ago
10

Find the amount of empty space within a cylinder containing three solid spheres, where each sphere has a radius of 3 cm. (Volume

of a sphere =43πr3) A. 54π cm3 B. 72π cm3 C. 126π cm3 D. 378π cm3
Mathematics
1 answer:
aalyn [17]3 years ago
5 0

Answer : The correct option is, (A) 54\pi cm^3

Step-by-step explanation :

First we have to calculate the volume of cylinder.

Formula used:

Volume of cylinder = \pi r^2h

where,

r = radius = 3 cm

h = height = 18 cm   (We are assuming that 3 solid spheres stacked to each other = 3 × diameter of each sphere = 3 × 2 × 3 = 18)

Volume of cylinder = \pi (3cm)^2\times (18cm)

Volume of cylinder = 162\pi cm^3

Now  we have to calculate the volume of 3 solid spheres.

Formula used:

Volume of 3 spheres = 3\times \frac{4}{3}\pi r^3

Volume of 3 spheres = 4\pi r^3

Volume of 3 spheres = 4\pi (3)^3

Volume of 3 spheres = 108\pi cm^3

Now we have to calculate the amount of empty space within a cylinder.

Amount of empty space within a cylinder = Volume of cylinder - Volume of 3 spheres

Amount of empty space within a cylinder = 162\pi cm^3-108\pi cm^3

Amount of empty space within a cylinder = 54\pi cm^3

Therefore, the amount of empty space within a cylinder is, 54\pi cm^3

You might be interested in
I need help on this question
storchak [24]
It’s the third one.. I think
7 0
3 years ago
Read 2 more answers
Simplify the expression. 9r 3r2 – 5r 7
Ksenya-84 [330]
Your final answer is going to be 4r + 3r ^2 +7
7 0
3 years ago
Read 2 more answers
Using differential calculus, maximize the volume of a box made of cardboard (top is open) as shown in Figure A. 15, subject to t
lana [24]

The maximum volume of the box is 40√(10/27) cu in.

Here we see that volume is to be maximized

The surface area of the box is 40 sq in

Since the top lid is open, the surface area will be

lb + 2lh + 2bh = 40

Now, the length is equal to the breadth.

Let them be x in

Hence,

x² + 2xh + 2xh = 40

or, 4xh = 40 - x²

or, h = 10/x - x/4

Let f(x) = volume of the box

= lbh

Hence,

f(x) = x²(10/x - x/4)

= 10x - x³/4

differentiating with respect to x and equating it to 0 gives us

f'(x) = 10 - 3x²/4 = 0

or, 3x²/4 = 10

or, x² = 40/3

Hence x will be equal to 2√(10/3)

Now to check whether this value of x will give us the max volume, we will find

f"(2√(10/3))

f"(x) = -3x/2

hence,

f"(2√(10/3)) = -3√(10/3)

Since the above value is negative, volume is maximum for x = 2√(10/3)

Hence volume

= 10 X 2√(10/3)  -  [2√(10/3)]³/4

= 2√(10/3) [10 - 10/3]

= 2√(10/3) X 20/3

= 40√(10/27) cu in

To learn more about Maximization visit

brainly.com/question/14682292

#SPJ4

Complete Question

(Image Attached)

3 0
1 year ago
Area= 18yd squared, length= 6yd<br> width=
GenaCL600 [577]

Answer:

The width is 3 yds

Step-by-step explanation:

Area = length * width

18 = 6*w

Divide each side by 6

18/6 = 6w/6

3=w

The width is 3 yds

7 0
3 years ago
Which only lists multiples of 16? O1,2,4, 8, 16 O 16, 24, 32, 40 O16, 32, 48, 64 O 1,2, 4, 8, 12, 16​
schepotkina [342]

Answer:

48 & 68

Step-by-step explanation:

if you multiply the numbers you will see that you get 48 & 68 multiple times

5 0
3 years ago
Other questions:
  • Which statements are true about
    8·1 answer
  • Why is pi measured as 3.14?
    9·2 answers
  • What is the answer to 15 divided by 1 2/3
    11·1 answer
  • One cubic foot of water weighs about 62.4 pounds. How many pounds of water can the fish tank hold when it is full? Length is 2.5
    15·1 answer
  • Can someone please help me on this?
    13·1 answer
  • Line AB is tangent to circle O. If AO = 24 and BC = 50, what is AB? PLS HELP THANKYOU
    9·2 answers
  • D=rt help solve for r
    6·1 answer
  • Find three consecutive even integers have a sum of 48.
    13·2 answers
  • Answer the following questions using the table below.
    8·1 answer
  • Help me solve this problem plsssss ​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!