Reema was very excited about her birthday as only two days were left for her birthday party. She was telling her tuition teacher about her birthday party and also shown the things purchased by her for the birthday party such as candles, sweets, caps, cold drink cans, fruit juice bottles etc. Her tuition teacher asked Reema to bring caps and cylindrical containers which they have purchased as she was teaching her “Mensuration Topic”. They observed the cylindrical container has 220cm circumference and 14cm height. Conical cap has radius of 15cm and vertical height 20cm. On the basis of above information, answer the following questions: (i) How much fruit juice can be filled in cylinder? (ii) Find out the C.S.A and volume of conical cap.

Answer:

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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]

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