Question

it cost Rs 4400 to paint the inner curved surface of cylindrical
can 10 m deep. If the cost of painting is at the rate of Rs 20 per
square metre. Find
5 marks
(1) inner curved surface area of the vessel,
(ii) radius of the vessel
(iii) capacity of the vessel​

Plz answer it fast and correctly

Answer 1

QuestioN :

it cost Rs 4400 to paint the inner curved surface of cylindrical can 10 m deep. If the cost of painting is at the rate of Rs 20 per square metre. Find

(i) inner curved surface area of the vessel,

(ii) radius of the vessel

(iii) capacity of the vessel​

GiveN :

• It cost Rs 4400 to paint the inner curved surface of cylindrical  can 10 m deep.
• The cost of painting is at the rate of Rs 20 per  square meter.

To FiNd :

• inner curved surface area of the vessel,

• radius of the vessel

• capacity of the vessel

ANswer :

1. Inner curved surface area of vessel = 220 m²
2. Radius of vessel = 3.5 m.
3. Capacity of vessel = 385 m³

SolutioN :

1).

Cost of painting = Rs. 4400

Rate of painting​  = Rs. 20/m²

Now,

⇒ Inner CSA of vessel = Cost of painting/Rate of painting

⇒ Inner CSA of vessel = 4400/20

⇒ Inner CSA of vessel = 220 m²

∴ Inner curved surface area of vessel = 220 m²

2).

Now, CSA of cylinder = 2πrh

So atq,

⇒ 2πrh = 220

⇒ 2 * 22/7 × r × 10 = 220

⇒ 440r/7 = 220

⇒ 440r = 220 × 7

⇒ 440r = 1540

⇒ r = 1540/440

⇒ r = 3.5 m

∴ Radius of vessel = 3.5 m.

3).

Now, we have, r = 3.5m , h = 10 m.

⇒ Capacity of cylinder = πr²h

⇒ Capacity of vessel = 22/7 ×(3.5)² × 10

⇒ Capacity of vessel = 22/7 × 12.25 × 10

⇒ Capacity of vessel = 385 m³

∴ Capacity of vessel = 385 m³

Answer 2

$\underline\blue{\bold{Given \: Question :- }}$

• It cost Rs 4400 to paint the inner curved surface of cylindrical can 10 m deep. If the cost of painting is at the rate of Rs 20 per square metre. Find
• (1) inner curved surface area of the vessel,
• (ii) radius of the vessel
• (iii) capacity of the vessel7

$\huge \orange{AηsωeR} ✍$

$\underline\blue{\bold{Given :- }}$

• Height of cylindrical can is 10 m
• It cost it cost Rs 4400 to paint the inner curved surface of cylindrical of can at the rate of Rs 20 per square metre.

$\underline\blue{\bold{To \: Find :- }}$

• (i) inner curved surface area of the vessel,
• (ii) radius of the vessel
• (iii) capacity of the vessel

$\underline\blue{\bold{ Formula \: Used :- }}$

${{ \boxed{{\bold\green{Curved \: Surface \: Area_{(Cylinder)}\: = \:2\pi rh)}}}}}$

${{ \boxed{{\bold\red{Volume_{(Cylinder)}\: = \:\pi r^2 h }}}}}$

${ \boxed {\bf{Solution}}}$

$\begin{gathered}\begin{gathered}\bf Let = \begin{cases} &\sf{r \: be \: the radius \: of \: cylinder} \\ &\sf{h \: be \: the \: height \: of \: cylinder} \end{cases}\end{gathered}\end{gathered}$

$\bf \:\large \red{AηsωeR : 1} ✍$

$\bf \:Total \: cost \: of \: paint \:can = Rs \: 4400$

$\bf \:Cost \: of \: paint/ {m}^{2} =Rs \: 20$

$\bf \:Height \: (h) \: of \: cylindrical \: can \: is \: 10 \: m$

$\bf \:  ⟼ Inner \: curved \: surface \: area \: painted \: </p><p></p><p>$

$\bf \: = \dfrac{total \: cost}{Cost \: per \: {m}^{2} }$

$\bf \: = \dfrac{4400}{20}$

$\bf \: = 220 \: {m}^{2}$

__________________________________________

$\bf \:\large \red{AηsωeR : 2} ✍$

$\bf \:Inner \: curved \: surface \: area \: = 220 \: {m}^{2}$

$\bf\implies \:2\pi \: rh = 220$

$\bf\implies \:2 \times \dfrac{22}{7} \times r \times 10 = 220$

$\bf\implies \:r = \dfrac{7}{2} \: m$

__________________________________________

$\large \red{AηsωeR : 3} ✍$

${{ {\large{\bold\red{Volume_{(Cylinder)}\: = \:\pi r^2 h }}}}}$

$\bf \: = \dfrac{22}{7} \times \dfrac{7}{2} \times \dfrac{7}{2} \times 10$

$\bf \: = 385 \: {m}^{3}$

${{ {\large{\bold{Volume_{(Cylinder)}\: = \:385 \: {m}^{3} }}}}}$

___________________________________________

More information:-

Perimeter of rectangle = 2(length× breadth)

Diagonal of rectangle = √(length²+breadth²)

Area of square = side²

Perimeter of square = 4× side

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²