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
Veronika [31]
3 years ago
15

Q2.What is the ratio of volumes of the two cylinders formed by rolling a sheet of dimensions lxb in two different ways? Q3.What

is the height of a right circular cylinder made from a rectangular sheet of length 20cm and breadth 15cm if it’s rolled along its length? Q4.What is the curved surface area of a cylinder obtained by rolling a square along its 7cm long side? Q5.What is the ratio of the total surface area and the curved surface area of the cylinder?
Mathematics
1 answer:
Kobotan [32]3 years ago
5 0

Answer:

2. b : l

3. 20cm

4. 49 cm^{2}

5. (2\pi+1):2\pi

Step-by-step explanation:

<u>Solution 2:</u>

Let cylinder is rolled along 'l':

Height of cylinder , h = length of rectangle = l

Perimeter of base = b

Let 'r' be the radius of cylinder's base:

2\pi r = b\\\Rightarrow r = \dfrac{b}{2\pi}

Volume of a cylinder is given as:

V = \pi r^{2} h

Putting the values:

V_1 = \pi (\dfrac{b}{2\pi})^2 l\\\Rightarrow V_1 =  (\dfrac{b^2}{4\pi}) l

Let cylinder is rolled along 'b':

Height of cylinder , h = length of rectangle = b

Perimeter of base = l

Let 'r' be the radius of cylinder's base:

2\pi r = l\\\Rightarrow r = \dfrac{l}{2\pi}

Volume of a cylinder is given as:

V = \pi r^{2} h

Putting the values:

V_2 = \pi (\dfrac{l}{2\pi})^2 b\\\Rightarrow V_2 =  (\dfrac{l^2}{4\pi}) b

Taking ratio:

V_1:V_2 = \dfrac{(\dfrac{b^2}{4\pi}) l}{(\dfrac{l^2}{4\pi}) b} = b:l

Solution 3:

Rectangle is rolled along its length to make a cylinder, so height will be equal to its length.

\therefore height of cylinder = 20 cm

Solution 4:

Side of square = 7 cm

Height of cylinder =Side of square = 7 cm

7 cm will be the circumference of the circle.

i.e. 2\pi r = 7 cm

Curved surface area of a cylinder:

CSA = 2\pi rh

Putting the above values:

CSA = 7 \times 7 = 49 cm^{2}

Solution 5:

As calculated in above step:

CSA = 2\pi rh = 7 \times 7 = 49 cm^{2}

Total surface area = 2\pi r^{2} + 2\pi r h

Calculating value of r:

2\pi r = 7 cm

\Rightarrow 2  \pi r = 7\\\Rightarrow r = \dfrac{7}{2\pi}

Total surface area =

2\pi (\dfrac{7}{2\pi})^{2} + 49\\\Rightarrow \dfrac{49}{2\pi}+49\\\Rightarrow 49(\dfrac{1}{2\pi}+1) cm^2

Ratio of TSA: CSA is

49(\dfrac{1}{2\pi}+1) cm^2 : 49 cm^2\\\Rightarrow (\dfrac{1}{2\pi}+1):1\\\Rightarrow (2\pi+1): 2\pi

You might be interested in
rope price of length 45cm 25 cm and 81 cm have to be cut into same size pieces what is the smallest price length possible​
Sergeeva-Olga [200]

= 2025

When you are told to find the smallest length possible, you perform L.C.M(Least common multiples)

For this, you divide the given lengths using the numbers that divides all through.

I have added an image to this answer. Go through it for more explanation

5 0
2 years ago
A cell phone bill provider offers a plan that costs $20 per month plus $0.10 per text message sent or received. A comparable pla
dybincka [34]

Answer:

100 texts

Step-by-step explanation:

20+.1x=30

30-20=10

10 dollar difference in base prices.

10/.1 (to find out how many texts)

100 texts

7 0
3 years ago
DIG DEEPER! A truck produces 22 pounds of carbon dioxide for every gallon of diesel
Illusion [34]

Answer:

y=22    x=18

Step-by-step explanation:

4 0
2 years ago
Find the values of a and b that make the quadrilateral a parallelogram.
Yuri [45]

Step-by-step explanation:

both halves of a diagonal must be equal.

so,

8b - 30 = 6b + 6

2b = 36

b = 18

and

9a - 13 = 5a + 5

4a = 18

a = 18/4 = 4.5

5 0
1 year ago
5+5 What is it........................................
Elza [17]

Answer:

I dont even want to answer this cause I know its a joke

Step-by-step explanation:

5+5=10

7 0
2 years ago
Other questions:
  • What is the number of square inches in one square foot?
    14·1 answer
  • A Hippopotamus can run 6 kilometers in 15 minutes. At this rate how far can the hippopotamus run in 1 minute
    5·1 answer
  • Draw a shape using a rectangle and a triangle
    6·1 answer
  • Identify the degree of the polynomial 4xy-11y-3
    7·2 answers
  • Mr. Gail uses 12 gallons of gas for a 400-mile trip. How far can I travel on one gallon of gas​
    6·1 answer
  • Pls help me with this statistic assignment
    11·1 answer
  • If 75% of a number is 165 and 10% of the same number is 22, find 85% of that number.
    15·1 answer
  • Is it Substitution or linear combination?​
    15·1 answer
  • 6^9+6^8)/(6^8*6^-9)<br>HELP PLS​
    13·2 answers
  • HELP Please<br>I really need the answer​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!