Question

the length and breadth and height of a rectangular solid are in the ratio 5:4:2. If total surface area is 1216cm².fi d the volume of the solid​

Answer 1

Answer:

Volume of the solid = 2,560 cm³

Step-by-step explanation:

Let the ratio be 5x , 4x, 2x respectively.

Rectangular solid means it is in the shape of a cuboid.

Total surface area of cylinder = 2(lb + bh + hl) = 1216cm²

Here,

• l = length
• b = breadth
• h = height

$\therefore \qquad\rm 2[5x(4x) + 4x(2x) + 2x(5x)] = 1,216cm^2$

$\dashrightarrow\rm 2[20x^2 + 8x^2 +10x^2] = 1,216cm^2$

$\dashrightarrow\rm 20x^2 + 8x^2 +10x^2 = \dfrac{1,216cm^2}{2}$

$\dashrightarrow\rm 38x^2 = 608cm^2$

$\dashrightarrow\rm x^2 = \dfrac{608cm^2}{38}$

$\dashrightarrow\rm x^2 = 16cm^2$

$\dashrightarrow\rm x = \pm\sqrt{16cm^2}$

$\dashrightarrow\rm x = \pm 4cm$

x = 4 or x = -4

But dimensions can't be negative, therefore x = 4 is valid.

• Length = 5x = 5(4cm) = 20cm
• Breadth = 4x = 4(4cm) = 16cm
• Height = 2x = 2(4cm) = 8cm

Volume of Cuboid = 20cm × 16cm × 8cm = 2,560cm³