The dimension of rectangular parallelopiped are in the ratio 6 : 5 : 4

1.	The dimension of rectangular parallelopiped are in the ratio 6 : 5 : 4 and its total surface area is 33300 square metres. Find its volume.
Answer» Let length, breadth and height of a cuboid are 6x, 5x and 4x respectively. Its total surface area = 2(lb + bh + hl) = 2(6x × 5x + 5x × 4x + 4x × 6x) = 2(30 x 2 + 20 x 2 + 24 x 2) = 2 x 74 x 2 = 148 x 2 But it is given that total surface area = 333000 sq.m i.e. 148 x 2 = 33300 ⇒ x² = \(\frac { 33300 }{ 148 }\) ⇒ x² = 225 m² ⇒ x = √225 ⇒ x = 15 m Dimensions of cuboid are 6x = 6 × 15 = 90 m 5x = 5 × 15 = 75 m and 4x = 4 × 15 = 60 m Volume of cuboid = 90 × 75 × 60 cubic metres = 405000 cubic metres.

The dimension of rectangular parallelopiped are in the ratio 6 : 5 : 4 and its total surface area is 33300 square metres. Find its volume.

Answer»

Let length, breadth and height of a cuboid are 6x, 5x and 4x respectively.

Its total surface area

= 2(lb + bh + hl)

= 2(6x × 5x + 5x × 4x + 4x × 6x)

= 2(30 x 2 + 20 x 2 + 24 x 2)

= 2 x 74 x 2

= 148 x 2

But it is given that total surface area = 333000 sq.m

i.e. 148 x 2 = 33300

⇒ x² = \(\frac { 33300 }{ 148 }\)

⇒ x² = 225 m²

⇒ x = √225

⇒ x = 15 m

Dimensions of cuboid are

6x = 6 × 15 = 90 m

5x = 5 × 15 = 75 m

and 4x = 4 × 15 = 60 m

Volume of cuboid = 90 × 75 × 60 cubic metres

= 405000 cubic metres.