Question

12. The dimensions of a cuboid are in ratio 4:3:1. If it's volume is 6144 m3, Find the total surface area of cuboid.​

Answer 1

Answer:

Given,

Volume of a cuboid is 6144 cu. m

Ratio of dimension of a cuboid is 4:3:1

Here, x be the common part

Therefore,

Length (L) = 4×x = 4x m

Breadth (B) = 3×x = 3x m

Height (H) = 1×x = x m

Total Surface Area (T.S.A) = ?

A.T.Q,

Volume of a cuboid = 6144 cu. m

or, L × B × H = 6144

or, 4x × 3x × x = 6144

or, 12x^3 = 6144

or, x^3 = 6144/12

or, x^3 = 512

or, x = (cubic√512)

or, x = (cubic√8×8×8)

or x = 8

Therefore,

Length = 4x = 4×8 = 32 m

Breadth = 3x = 3×8 = 24 m

Height = x = 8 m

By formula,

T.S.A of cuboid = 2×(LB+BH+HL)

= 2×(32×24 + 24×8 + 8×32) sq. m

= 2×(768 + 192 + 256) sq. m

= 2 × 1216 sq. m

= 2432 sq. m

Answer :- The total surface area of cuboid is

2432 sq. m