The length, breadth and height of a cuboidal box are in the ratio 7 : 5 : 3 and its whole surface area is 27832 cm2. its volume is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 288120 cm2
Let the sides of the cuboid be 7x, 5x & 3x.
⇒ The surface area of the cuboid = 2[lb + bh + hl]
⇒ A = 2[7x × 5x + 5x × 3x + 7x × 3x]
⇒ 27832 =2[ 35x2 + 15x2 + 21x2]
⇒ 142x = 27832
⇒ x2 = 196
⇒ x = 14 cm
The sides of the cuboid will be 98cm, 70cm & 42cm
⇒ The volume of the cube = lbh
⇒ V = 98 × 70 × 42
⇒ V = 288,120 cm3