Question

The length, breadth and height of a cuboid
(rectangular solid) are 4:3 : 2.
(i) If its surface area is 2548 cm², find its
volume.
(ii) If its volume is 3000 m³, find its surface
area.​

Answer 1

Surface area of cuboid = 2548 cm2

Ratio in length, breadth and height of a cuboid = 4 : 3 : 2

Let length = 4x, Breadth = 3x and height = 2x

∴ Surface area = 2(4x × 3x + 3x × 2x + 2x × 4x)

= 2(12x2 + 6x2 + 8x2)

= 2 × 26x2 = 52x2

∴ 52x2 = 2548

X2 = 2548/52 = 49 = (7)2

∴ x = 7

∴ Length = 4x = 4 × 7 = 28 cm

Breadth = 3x = 3 × 7 = 21 cm

And height = 2x = 2 × 7 = 14 cm

∴ Volume = lbh

= 28 × 21 × 14 cm3 = 8232 cm2

(ii) If volume = 3000 m3

⇒ 4x × 3x × 2x = 3000

⇒ 24x3 = 3000

⇒ x3 = 3000/24 = 125 = (5)3

∴ x = 5 m

Length = 5 × 4 = 20, Breadth = 5 × 3 = 15 m

And height = 5 × 2 = 10 m

∴ Surface area = 2[lb + bh + hl]

= 2[20 × 15 + 15 × 01 + 10 × 20] m2

= 2[300 + 150 + 200] m2

= 2 × 650 = 1300 m2