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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

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