Question

The ratio of lenghth,bradth and height of a solid cuboid is 4:3:3.Then the T.S.A is 468,find volume

Answer 1

Answer:

In this question the ratio of length, breadth & height is 4:3:2 not 4:3:3

Given,

Total surface area (TS.A) = 468 sq. unit

Ratio of length, breadth & height of a solid cuboid is 4:3:2

Here, X be the common part

Therefore,

Length(L) = 4 × X = 4X unit

Breadth(B) = 3× X = 3X unit

Height(H) = 2 × X = 3X unit

A.TQ,

T.S.A of a cuboid = 468

or, 2(LB + BH + HL) = 468

or, 2 (4X × 3X + 2X × 3X + 2X × 4X) = 468

or, 2 ( 12X^2 + 6X^2 + 8X^2) = 468

or, 2 × 26X^2 = 468

or, 52X^2 = 468

or, X^2 = 468/52

or, X^2 = 9

or, X = √9

or, X = 3

Therefore,

Length = 4X = 4 × 3 = 12 unit

Breadth = 3X = 3 × 3 = 9 unit

Height = 2X = 2 × 3 = 6 unit

By formula,

Volume of a solid cuboid = L × B × H

= 12 × 9 × 6 cu. unit

= 648 cu. unit

Answer :- The volume of a solid cuboid is 648 cu. unit