Question

It costs 3300 to paint the inner curved surface of a cylindrical vessel
10 m deep at the rate of 30 per m². Find the
(1) inner curved surface area of the vessel,
(ii) inner radius of the base, and
(iii) capacity of the vessel.​

Answer 1

Answer:

Height =10m

Total cost of painting =rupes 3300

Rate=ripped 30 per sq.m

Inner curved surface area =total cost/rate

=3300/30

=110sq.m

Inner curved surface area =2×pie×r×h

2×22/7×r×10=110

r=110×7/10×2×22

r=7/4

Diameter,d=7/4×2

=3.5

Volume=pie×r^2×h

=22/7×7/4×7/4×10

=77×5/4

=96.25 cubic m

1 cubic meter = 1kl

96.25 cubic metres =96.25kl

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Answer 2

Solution :

$\underline{\bf{Given\::}}}}$

• Cost of painting = Rs.3300
• The rate of painting = Rs.30/m²
• Height of cylindrical vessel, (h) = 10 m

$\underline{\bf{Explanation\::}}}}$

• Inner curved surface area of the vessel :

$\longrightarrow\sf{Cost\:of\:paint=Curved\:surface\:area\:of\:vessel\:\times rate\:of\:paint}\\\\\longrightarrow\sf{Rs.3300=Curved\:surface\:area\:of\:vessel\times 30/m^{2} }\\\\\longrightarrow\sf{Curved\:surface\:area\:of\:vessel=\cancel{3300/30}\:m^{2} }\\\\\longrightarrow\sf{Curved\:surface\:area\:of\:vessel=110\:m^{2} }$

• Inner radius of the base :

We know that formula of the curved surface area of cylinder;

$\boxed{\bf{C.S.A=2\pi rh\:\:\:\:(sq.unit)}}}}$

$\longrightarrow\sf{2\pi rh=110}\\\\\longrightarrow\sf{2\times 22/7\times r\times 10=110}\\\\\longrightarrow\sf{44/7\times r\times 10=110}\\\\\longrightarrow\sf{440/7\times r=110}\\\\\longrightarrow\sf{r=\cancel{110}\times 7/\cancel{440}}\\\\\longrightarrow\bf{r=7/4\:m}$

• Capacity of the vessel :

We know that formula of the volume of cylinder :

$\boxed{\bf{Volume=\pi r^{2} h\:\:\:\:(cubic\:unit)}}}}$

$\longrightarrow\sf{Volume=\pi r^{2} h}\\\\\longrightarrow\sf{Volume=\dfrac{22}{7} \times \bigg(\dfrac{7}{4} \bigg)^{2} \times 10}\\\\\\\longrightarrow\sf{Volume=\dfrac{22}{\cancel{7}} \times \dfrac{\cancel{49}}{16} \times 10}\\\\\\\longrightarrow\sf{Volume=\dfrac{22\times 7\times 10}{16} }\\\\\longrightarrow\sf{Volume=\cancel{1540/16}}\\\\\longrightarrow\bf{Volume=96.25\:m^{3} }$