Question

find the total surface area of an open tank of radius 6.3 m and height 3.5 m.how many litres of water can it hold
please ans fast and with calculation​

Answer 1

Answer:

Total surface area of the tank = 263.34 m²

Litres of water tank can hold = 436590 L

Step-by-step explanation:

Given:

• Radius of the tank = 6.3 m
• Height of the tank = 3.5 m

To Find:

• The total surface area
• Litres of water the tank can

Theory:

Here the radius and height of the tank is given. We have to substitute these datas in the formula for finding the TSA of the cylinder and solve it accordingly. To find the litres of water it can hold, the volume must be converted from m³ to litres.

Solution:

Here the tank is in the shape of a cylinder with the top open.

First we have to find the total surface area of the cylinder.

The total surface area of a cylinder is given by,

TSA of a cylinder  = 2π r (r + h)

    where r = radius of the cylinder

               h = height of the cylinder

But here since the tank is open, the top surface area must be subtracted.

The top area is in the shape of a circle.

    ∴ The area of top surface is πr².

Hence,

  TSA of the tank =  2 π r (r + h) - π r²

Substituting the data,

    $\sf{TSA\:of\:the\:tank=2\times \dfrac{22}{7}\times 6.3(6.3+3.5)-\dfrac{22}{7}\times (6.3)^{2}}$

    $\sf{TSA\:of\:the\:tank=2\times \dfrac{22}{7}\times 6.3\times 9.8-\dfrac{22}{7}\times 39.69}$

  Taking 22/7 as common,

    $\sf{TSA\:of\:the\:tank=\dfrac{22}{7}\bigg(123.48-39.69\bigg)}$

    $\sf{TSA\:of\:the\:tank=\dfrac{22}{7}\times 83.79}$

     $\sf{TSA\:of\:the\:tank=263.34\:m^{2} }$

∴ The TSA of the tank is 263.34 m².

   $\boxed{\bold{Total\:surface\:area\:of\:the\:tank=263.34\:m^{2}}}$

Now we have to find the volume of the tank.

Volume of a cylindrical tank is given by,

    Volume of the tank = π r² h

 Substitute the data,

    $\sf{Volume\:of\:the\:tank=\dfrac{22}{7}\times (6.3)^{2}\times 3.5}$

    $\sf{Volume\:of\:the\:tank=\dfrac{22}{7}\times 138.915}$

    $\sf{Volume\:of\:the\:tank=436.59\:m^{3} }$

Hence volume of the tank is 436.59 m³

Now we have to find the volume in litres

We know that,

    1 m³ = 1000 L

   Hence,

   436.59 m³ = 436590 L

∴ The tank can hold 436590 litres of water.

   $\boxed{\bold{Litres\:of\:water\:tank\:can\:hold=436590\:litres}}$