Question

A rectangular tank has length = 4 m, width = 3 m and capacity = 30 m ².A small model tank is made with capacity 240 cm³. Find:

I: the dimensions of the model

II:the ratio between the total surface area of the tank and its model.?

Answer 1

Step-by-step explanation:

Volume of cuboid is = l×b×h

1m² = 10⁴cm²

also,

the area of rectangular = l×b

According to question,

volume= l×b×h=30m²

Answer 2

Answer:

Hey mate here is your answer:

$\huge\boxed{\tex{Solution : }}$

→For the tank:

  Its length × breadth × height = Volume,

  ⇒     4 m × 3 m × height = 30 m³,

  ⇒      Height = $\large\boxed{\tex{\frac{30}{4*3} m = 3.5 m.}}$

  Let the scale factor for reduction = k,

   ∴Volume of the model=k³×volume of the tank,

   ⇒ 240 cm ³ = k³ × 30 m³,

   ⇒ 240 cm³ = k³×30×100×100×100 cm³,

   ⇒   $\large\boxed{k^3=\frac{240}{30*100*100*100}}$,

   ⇒$\large\boxed{\frac{1}{125000}}$,

    →Sector factor , k = $\large\boxed{\frac{1}{50}}$.

$\huge\red\boxed{(i)}$    :   Length of the model = k × length of the tank,

              $\large\boxed{\frac{1}{50}*4m =8cm}$,

            : Breadth of the model = k × breadth of the tank,

             $\large\boxed{\frac{1}{50}*3m=6\:cm}$,

And, height of the model:

             

                   $\large\boxed{\frac{1}{50}*2.5m=5cm}$,

∴$\large\boxed{Dimensions\: of\: the\: model=8 cm*6 cm* 5 cm}$.

$\huge\boxed{(ii)}$  :  

    →Since , total surface area of the model = k²×total S.A of the tank

    ⇒ $\large\boxed{\frac{Total \:S.A \:of\: the\: tank}{Total\: S.A \:of\: the\: model}}$   $\large\boxed{=}$   $\large\boxed{\frac{1}{k^2} = (50)^2}$,

    = 2500.

$\huge\boxed{So\:ratio=2500:1}$.

$\huge\boxed{Hope\:it\:helps\:you}$.