Question

39. The length, breadth and height of a cuboid are in the
ratio 5:4:2 and the total surface area is 1216 cm?,
then the volume of the cuboid is
(A) 2460 cm
(B) 2560 cm
(C) 2660 cm
d 2700 cm​

Answer 1

Answer:

$2(20x {}^{2} + 8 {x}^{2} +10 {x}^{2}) = 1216 \\ 2(38x {}^{2} ) =1216 \\ 76x {}^{2} = 1216 \\ {x}^{2} = \frac{1216}{76} \\ {x }^{2} = 16 \\ x = 4 \\ l = 20cm \\ b = 16 \\ h = 8 \\ = 20 \times 16 \times 8 \\ = 2560 \\ option)b$

Answer 2

Answer:

Answer:

Option (b) is correct. Volume of cubiod is 2560 cm³.

Step-by-step explanation:

Given :-

Length, Breadth and height of cubiod are in ratio of 5:4:2.

Total surface area of cuboid is 1216 cm².

To find :-

Volume of cubiod.

Solution :-

Let, Dimensions be :

Length be 5x.

Breadth be 4x.

Height be 2x.

Total surface area of cuboid = 2(lb + bh+ lh)

Where,

l, b and h are length, breadth and height of cuboid.

Put values :

\longrightarrow ⟶ 1216 = 2× [(5x × 4x)+(4x × 2x)+(2x × 5x)]

\longrightarrow ⟶ 1216 = 2 × [20x² + 8x² + 10x²]

\longrightarrow ⟶ 1216 = 40x² + 16x² + 20x²

\longrightarrow ⟶ 1216 = 76x²

\longrightarrow ⟶ 1216/76 = x²

\longrightarrow ⟶ 16 = x²

\longrightarrow ⟶ √16 = x

\longrightarrow ⟶ x = 4

So,

Dimensions :-

Length = 5x = 5×4 = 20 cm

Breadth = 4x = 4 × 4 = 16 cm

Height = 2x = 2 × 4 = 8 cm

Now,

We know,

Volume of cubiod = lbh

Put values:

\longrightarrow ⟶ Volume = 20 × 16 × 8

\longrightarrow ⟶ Volume = 2560

Therefore,

Volume of cubiod is 2560 cm³.

this is answer for your upper question.