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
Nastasia [14]
2 years ago
13

From a circular cylinder of diameter 10 cm and height 12 cm are conical cavity of the same base radius and of the same height is

hollowed out. Find the volume and the whole surface of the remaining solid.
(take \ \: \pi \:  = 3.14)


​
Mathematics
1 answer:
Nataliya [291]2 years ago
6 0
<h3>Volume of the remaining solid = 628 cm^2</h3>

<h3>Whole surface area = 659.4 cm^2</h3>

Step-by-step explanation:

Now, Given that:-

Diameter (d) = 10 cm

So, Radius (r) = 10/2 = 5cm

Height of the cylinder = 12cm.

volume \: of \: the \: cylinder \:  =  \pi {r}^{2} h

=  > \pi \times  {5}^{2} \times  12 {cm}^{3}   = 300\pi {cm}^{3}

Radius of the cone = 5 cm.

Height of the cone = 12 cm.

slant \: height \: of \: the \: cone \:  =  \sqrt{ {h}^{2}  + \:  {r}^{2} }

=  >  \sqrt{ {5}^{2}+{12}^{2} } cm \:  = 13cm

Volume of the cone = 1/3 *πr^2h

=  >  \frac{1}{3} \pi \times  {5}^{2}   \times 12 {cm}^{3}  = 100\pi {cm}^{3}

therefore, the volume of the remaining solid

= 300\pi {cm}^{3}  - 100\pi {cm}^{3}  \\  = 200 \times 3.14 {cm}^{3}  = 628 {cm}^{3}

Curved surface of the cylinder =

2\pi \: rh \:  = 2\pi \times 5 \times 12 {cm}^{2}  \\  = 120\pi {cm}^{2} .

curved \: surface \: of \: the \: cone \:  = \pi \: rl \\  = \pi \times 5 \times 13 {cm}^{2}  \\  = 65\pi {cm }^{2} \\ area \: of \: (upper)circular \: base \: \\  of \: cylinder \:  =  \\ =  \pi \:  {r}^{2}  = \pi \times  {5}^{2}

therefore, The whole surface area of the remaining solid

= curved surface area of cylinder + curved surface area of cone + area of (upper) circular base of cylinder

= 120\pi {cm}^{2}  + 65\pi {cm }^{2}  + 25 \pi {cm}^{2}  \\  = 210 \times 3.14 {cm}^{2}  = 659.4 {cm}^{2}

<h3>Hope it helps you!!</h3>

You might be interested in
Tyron has 27 playlists on his iPod. Each playlist contains 35 songs. How many songs does Tyron have on all of his playlists?​
xeze [42]

Answer:

945 songs

Step-by-step explanation:

27*35=945

4 0
3 years ago
In the New York State daily lottery game, a sequence of 4 (not necessarily different) digits in the range of 0-9 is selected at
devlian [24]

Answer:

50.40% probability that all 4 are different.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Desired outcomes:

4 digits, all different

For the first digit, it can be any of them, so there are 10 possible

For the second digit, it can be any of them other than the first digit. So there are 9 possible.

For the third digit, it can be any of them, other than the first and the second. So there are 8 possible.

By the same logic, 7 possible digits for the fourth. So

D = 10*9*8*7 = 5040

Total outcomes:

4 digits, each can be any of them(10 from 0 - 9).

So

T = 10*10*10*10 = 10000

Probability:

p = \frac{D}{T} = \frac{5040}{10000} = 0.5040

50.40% probability that all 4 are different.

5 0
3 years ago
Can someone help me find X of this triangle? thanks :)
tino4ka555 [31]

Since it is an equilateral triangle, all of the sides are the same length.

So, x=14 :)

Hope this helps!

7 0
3 years ago
Read 2 more answers
Jon is making hamburgers for a church lunch. He has 42 2/3 lbs of ground beef. How many 1/3 pound hamburgers can he make using a
mote1985 [20]
He can make 128 burgers
7 0
3 years ago
Read 2 more answers
Which of the following is NOT a tax collected by the federal government? A. sales tax B. excise tax C. income tax D. payroll tax
Usimov [2.4K]
I believe the answer is B "excise tax" I think its this answer because I know that the goverment charges income tax, payroll tax, and sales tax.
4 0
3 years ago
Read 2 more answers
Other questions:
  • Romeo is using a common algorithm to find the product of 8,125 × 9. Drag the correct numbers to the problem to show the partial
    9·2 answers
  • Arc CD 2/3 of the circumstance of a circle. What is the radian measure of the central angle?
    14·1 answer
  • The area of a rectangular deck is 680 square feet. The deck’s width is 17 feet. What is its perimeter?
    8·2 answers
  • What is a asteroid belt,
    7·1 answer
  • Nicole has 27 cars available to rent.
    12·1 answer
  • Simplify (9x^4y^5+6xy^3) ➗3xy^2
    7·1 answer
  • 8ftx4ftx5ft what is the diameter
    11·1 answer
  • "You figure you can ride Ghost Wind, then get on. Just bring him back to the stable when you're finished so I can rub him down."
    14·2 answers
  • Audel started her homework at 9:10 she finished at 9:45 how long did she spend on her homework
    8·1 answer
  • An experiment requires the population of the bacteria to reach 2 million before the experiment can begin. The reproduction rate
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!