Answer:
(i) Fruit juice can be filled in cylinder [tex]= 53.9 l[/tex]
(ii) C.S.A of conical cap [tex]=1178.57cm^{2}[/tex]
volume of conical cap [tex]=4712.388cm^{3}[/tex]
Step-by-step explanation:
Given:
Circumference of a cylinderical container = 220cm
Height = 14cm
To find:
(i) How much fruit juice can be filled in cylinder.
(ii) To find the C.S.A and volume of conical cap.
Step 1
(i) volume of cylinder [tex]=\pi r^{2} h$[/tex]
Circumference of a cylinder = [tex]2\pi r[/tex]
From the given circumference, we get
[tex]220=2\pi r[/tex]
[tex]$220=2 \times \frac{22}{7} \times r$[/tex]
[tex]$\frac{44}{7} r=220$\\[/tex]
equating,
[tex]$7 \times \frac{44}{7} r=220 \times 7$[/tex]
[tex]$44 r=1540$[/tex]
[tex]$\frac{44 r}{44}=\frac{1540}{44}$[/tex]
we get, [tex]r=35[/tex]
volume of cylinder [tex]= $\pi r^{2} h$[/tex]
[tex]$V=\frac{22}{4} \times(35)^{2} \times 14$[/tex]
Multiply fractions,
[tex]$a \times \frac{b}{c}=\frac{a \times b}{c}$[/tex]
[tex]$V=\frac{22 \times 35^{2} \times 14}{7}$[/tex]
[tex]$V=\s(35)^{2} \times 44$[/tex]
[tex]V = 1225*44[/tex]
[tex]V = 53900 cm^{3}[/tex]
Fruit juice that can be filled [tex]= 1cm^{3}[/tex]
[tex]= 0.001l[/tex] [tex]= \frac{1}{1000} l[/tex]
Then we get, [tex]\frac{53900}{1000} = 53.9l[/tex]
Step 2
(ii) C.S.A of a conical cap [tex]= \pi rl[/tex]
[tex]$l=\sqrt{ r^{2}+h^{2}}$[/tex]
[tex]$l=\sqrt{ (15)^{2}+(20)^{2}}$[/tex]
[tex]=\sqrt{225+400}[/tex]
[tex]=\sqrt{625}[/tex]
[tex]=25cm[/tex]
Hence, C.S.A of a conical cap [tex]= \pi rl[/tex]
[tex]\pi rl =\frac{22}{7} \times(15) \times 25$[/tex]
[tex]$V=\frac{22 \times 15 \times 25}{7}$[/tex]
[tex]=1178.57cm^{2}[/tex]
Volume of conical cap[tex]=\frac{1}{3} h\pi r^{2}[/tex]
[tex]= \frac{1}{3} \pi *20*(15)^{2}[/tex]
[tex]$=\frac{4500 \pi}{3}$[/tex]
[tex]= 1500\pi[/tex]
[tex]=4712.388cm^{3}[/tex]
Therefore, C.S.A of conical cap [tex]=1178.57cm^{2}[/tex].
volume of conical cap [tex]=4712.388cm^{3}[/tex]
#SPJ3