Answer:
2. b : l
3. 20cm
4. 49 [tex]cm^{2}[/tex]
5. [tex](2\pi+1):2\pi[/tex]
Step-by-step explanation:
Solution 2:
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:
[tex]2\pi r = b\\\Rightarrow r = \dfrac{b}{2\pi}[/tex]
Volume of a cylinder is given as:
[tex]V = \pi r^{2} h[/tex]
Putting the values:
[tex]V_1 = \pi (\dfrac{b}{2\pi})^2 l\\\Rightarrow V_1 = (\dfrac{b^2}{4\pi}) l[/tex]
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:
[tex]2\pi r = l\\\Rightarrow r = \dfrac{l}{2\pi}[/tex]
Volume of a cylinder is given as:
[tex]V = \pi r^{2} h[/tex]
Putting the values:
[tex]V_2 = \pi (\dfrac{l}{2\pi})^2 b\\\Rightarrow V_2 = (\dfrac{l^2}{4\pi}) b[/tex]
Taking ratio:
[tex]V_1:V_2 = \dfrac{(\dfrac{b^2}{4\pi}) l}{(\dfrac{l^2}{4\pi}) b} = b:l[/tex]
Solution 3:
Rectangle is rolled along its length to make a cylinder, so height will be equal to its length.
[tex]\therefore[/tex] 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. [tex]2\pi r[/tex] = 7 cm
Curved surface area of a cylinder:
[tex]CSA = 2\pi rh[/tex]
Putting the above values:
CSA = 7 [tex]\times[/tex] 7 = 49 [tex]cm^{2}[/tex]
Solution 5:
As calculated in above step:
CSA = [tex]2\pi rh =[/tex] 7 [tex]\times[/tex] 7 = 49 [tex]cm^{2}[/tex]
Total surface area = [tex]2\pi r^{2} + 2\pi r h[/tex]
Calculating value of r:
[tex]2\pi r[/tex] = 7 cm
[tex]\Rightarrow 2 \pi r = 7\\\Rightarrow r = \dfrac{7}{2\pi}[/tex]
Total surface area =
[tex]2\pi (\dfrac{7}{2\pi})^{2} + 49\\\Rightarrow \dfrac{49}{2\pi}+49\\\Rightarrow 49(\dfrac{1}{2\pi}+1) cm^2[/tex]
Ratio of TSA: CSA is
[tex]49(\dfrac{1}{2\pi}+1) cm^2 : 49 cm^2\\\Rightarrow (\dfrac{1}{2\pi}+1):1\\\Rightarrow (2\pi+1): 2\pi[/tex]
