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:

• 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.

Answer 2

Gɪᴠᴇɴ :

• The length, breadth and height of a cuboid are in the ratio 5 : 4 : 2.

Lᴇᴛ,

• The length (l) of the cuboid is 5x.

• The breadth (b) of the cuboid is 4x.

• And the height (h) of the cuboid is 2x.

• The total surface area is 1216 cm².

Tᴏ Fɪɴᴅ :

• The volume of the cuboid.

Cᴀʟᴄᴜʟᴀᴛɪᴏɴ :

Wᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

↝ The total surface area (T.S.A) of cuboid is,

$\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{T.S.F\:=\:2\:(lb\:+\:bh\:+\:hl)\:}}}}}}$

$\longrightarrow\:\sf{1216\:=\:2\:(5x\times{4x}\:+\:4x\times{2x}\:+\:2x\times{5x})\:}$

$\longrightarrow\:\sf{1216\:=\:2\:(20x^2\:+\:8x^2\:+\:10x^2)\:}$

$\longrightarrow\:\sf{1216\:=\:2\times{38x^2}\:}$

$\longrightarrow\:\sf{76x^2\:=\:1216\:}$

$\longrightarrow\:\sf{x^2\:=\:\dfrac{1216}{76}\:}$

$\longrightarrow\:\sf{x\:=\:\sqrt{16}\:}$

$\longrightarrow\:\bf{x\:=\:4\:}$

Hᴇɴᴄᴇ,

✯ Length = 5x

➛ Length = 5 × 4

➛ Length = 20 cm

✯ Breadth = 4x

➛ Breadth = 4 × 4

➛ Breadth = 16 cm

✯ Height = 2x

➛ Height = 2 × 4

➛ Height = 8 cm

Nᴏᴡ,

Wᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

↝ Volume of the cuboid is,

$\pink\bigstar\:\:{\underline{\green{\boxed{\bf{\blue{Volume\:=\:l\times{b}\times{h}\:}}}}}}$

$:\implies\:\:\sf{Volume\:=\:20\times{16}\times{8}\:}$

$:\implies\:\:\bf\pink{Volume\:=\:2560\:cm^3}$

$\Large\bf{Therefore,}$

The volume of the cuboid is 2560 cm³.