Question

6. The dimensions of a cuboid are in the ratio 5:3 : 2. Find its total surface
given that its volume is 810 cm.
​

Answer 1

Answer:

558 cm²

Step-by-step explanation:

Let the ratio be 5x : 3x : 2x.

Volume of cuboid = l×b×h

Given volume = 810 cm³

=> 5x × 3x × 2x = 810

=> 30x³ = 810

=> x³ = 810/30

=> x³ = 27

=> x = 3

Hence, length = (5×3) cm = 15 cm.

Breadth = (3×3) cm = 9 cm.

Height = (2×3) cm = 6 cm.

Total Surface Area of cuboid = 2 (lb + bh + hl)

=> T.S.A. = 2 (15×9 + 9×6 + 6×15) cm²

=> T.S.A. = 2 (135 + 54 + 90) cm²

=> T.S.A. = 2 (279) cm² = 558 cm²