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:
Answer & explanation
Correct answer: option 1
We know that,
Total surface area of cuboid = 2(lb + bh + hl)
Volume of the cuboidal box = lbh
Ratio of length, breadth and height of cuboidal box = 7a : 5a : 3a
Total surface are of cuboidal box = 2 (7a × 5a + 5a × 3a + 3a × 7a) = 27832
= (35a2 + 15a2 + 21a2) = \(\frac{27832}{2}\)
= 71x2 = 13916
= a2 = 196
= a = \(\sqrt {196}\)
= a = 14
Volume of the cuboidal box = 7a × 5a × 3a = 105 × 14 × 14 × 14 = 288120