Question

length breadth and height of a room are in the ratio 5 ratio 4 ratio 2 if total surface area is 1216 cm² find volume ?

Answer 1

Given :- length breadth and height of a room are in the ratio 5:4:2
T.S.A of room = 1216 cm square

Let , length be 5x cm
breadth be 4x cm
height be 2x cm

$T.S.A = 1216 \\ = > 2( lb + bh + hl ) = 1216 \\ \\ = > 2(5x \times 4x + 4x \times 2x+2x \times 5x) = 1216 \\ \\ = > 2(20 {x}^{2} + 8 {x}^{2} + 10 {x}^{2} ) = 1216 \\ \\ = > 2(38 {x) }^{2} = 1216 \\ \\ = > 76 {x}^{2} = 1216 \\ \\ = > {x}^{2} = \frac{1216}{76} \\ \\ = > {x}^{2} = 16 \\ \\ = > x = \sqrt{16} \\ \\ = > x = 4$
So,
length = 5x = 5*4 = 20cm
breadth = 4x = 4*4 = 16cm
height = 2x = 2*4 = 8cm

Volume = length*breadth*height
= 20*16*8
= 2560

Hence volume = 2560 cm cube.