Question

The capacity of an open cylindrical tank is 2079m^3 and the diameter of its base is 21m. Find the cost of plastering its inner surface at 40 rupees per square metre.

Answer 1

Answer :-

• Cost of Plastering the inner CSA = 29700 Rs

Given :-

• Capacity of Cylindrical tank = 2079 m³
• Diameter of Cylindrical tank = 21 m
• Cost of Plastering per m² = 40 Rs

To Find :-

• Cost of Plastering the inner CSA = ?

Explanation :-

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In order to find the cost of Plastering the Tank, first we need to find the Radius of the Tank.

$\purple { \bf \bigstar \: Radius = \dfrac{Diameter}{2} \: \bigstar }$

$\rm \implies Radius = \dfrac{21}{2} \: m$

$\rm \implies Radius = 10.5 \: m$

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As per above data, We need to find the Height of tank, Let the Height of the Tank to be 'x' m

Capacity of tank is given that is equal to the Volume of the Cylindrical Tank.

$\purple { \bigstar \: \text{\bf Volume of Cylindrical Tank = Capacity of Cylindrical Tank} \: \bigstar }$

$\rm \leadsto \pi r^2h = 2079$

$\rm \leadsto \dfrac{22}{7} \times (10.5)^2 \times x = 2079$

$\rm \leadsto \dfrac{22}{7} \times 10.5 \times 10.5 \times x = 2079$

$\rm \leadsto 22 \times 1.5 \times 10.5 \times x = 2079$

$\rm \leadsto 33 \times 10.5 \times x = 2079$

$\rm \leadsto 346.5 \times x = 2079$

$\rm \leadsto x = \dfrac{2079}{346.5} = \dfrac{20790}{3465}$

$\blue { \boxed { \bf \leadsto x = 6 \: m }}$

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Now Finding the Area of plastering,

$\purple { \bigstar \: \text{\bf Area of plastering = CSA of Tank + Area of Base} \: \bigstar }$

$\rm \leadsto 2 \pi rh + \pi r^2$

$\rm \leadsto (2 \times \dfrac{22}{7} \times 10.5 \times 6) + (\dfrac{22}{7} \times 10.5 \times 10.5)$

$\rm \leadsto (2 \times 22 \times 1.5 \times 6) + (22 \times 1.5 \times 10.5)$

$\rm \leadsto (44 \times 9) + (33 \times 10.5)$

$\rm \leadsto (396) + (346.5)$

$\orange { \boxed { \bf \leadsto 742.5 \: m^2 }}$

Now Finding the cost,

$\rm \leadsto Cost \: of \: Plastering \: 1 \: m^2 = 40 \: R_S$

$\rm \leadsto Cost \: of \: Plastering \: 742.5 \: m^2$

         $\rm = (40 \times 742.5) \: R_S$

        $\red { \underline { \boxed { \bf = 29700 \: R_S }}}$

Hence, the cost of Plastering the Inner CSA of Cylindrical Tank is 29700 Rs.