Question

the whole surface of a rectangular solid is 448 sq.cm.the length of the solid is twice its breadth and the height is half its breadth.find the volume of the solid​

Answer 1

Answer:

The volume of rectangular solid is 896√14 cubic cm

Step-by-step explanation:

Given as

Area of rectangular solid = A = 448 sq cm

the breadth of solid = b cm

The length of solid = l = 2 b

The height of solid = h = $\dfrac{b}{2}$

Let The volume of solid = V cubic cm

According to question

∵  Area = 448 sq cm

Or. l × b = 448

Or, 2 × b × b = 448

Or, b ² =  $\dfrac{448}{2}$

i..e b² = 224

∴  b = √224

Or, b = 4 √14   cm

So, The breadth = b = 4 √14   cm

The length = 2 × b = 2 × 4 √14 = 8√14 cm

height = $\dfrac{4\sqrt{14} }{2}$ = 2√14  cm

Now,

Volume of rectangular solid = l × b  × h

Or, V = 8√14 cm × 4√14 cm  × 2√14 cm

∴    V = 896√14 cm³

Hence, The volume of rectangular solid is 896√14 cubic cm . Answer

Answer 2

The volume of the solid is 512 cubic. cm.

Step-by-step explanation:

We are given that the whole surface of a rectangular solid is 448 sq.cm.

Also, the length of the solid is twice its breadth and the height is half its breadth.

Let the breadth(B) of solid be $x$ cm.

So, the length(L) of the solid will be $2x$ cm and the height(H) of solid is $\frac{x}{2}$ cm.

Now, the whole surface area of the solid is given by;

        2[LB + BH + HL]  =  448 sq. cm

        2[ $2x(x) + x(\frac{x}{2})+\frac{x}{2}(2x)$ ]  =  448

            $2x^{2} +\frac{x^{2} }{2} +x^{2} = \frac{448}{2}$

             $3x^{2} +\frac{x^{2} }{2} = 224$

              $\frac{6x^{2}+ x^{2} }{2} = 224$

               $\frac{7x^{2} }{2} = 224$

                $x^{2} =\frac{224 \times 2}{7}$

                $x^{2} = 64$

So, x = 8 cm which means breadth of the solid is 8 cm.

Length of the solid = $2x$ cm = 16 cm

Height of the solid =  $\frac{x}{2}$ cm = 4 cm

Now, volume of the solid =  $L \times B \times H$

                                          =  $16 \times 8 \times 4$ = 512 $cm^{3}$.