Question

the dimensions of a cuboid are in the ratio of
4:3:1. If its total surface area is 3800 cm2,
then find its volume.​

Answer 1

$\huge{\underline{\boxed{\boxed{\red{\mathcal{QUESTION:}}}}}}$

The dimensions of a cuboid are in the ratio of  4 : 3 : 1. If its total surface area is 3800 cm²,  then find its volume.​

$\huge{\underline{\boxed{\boxed{\red{\mathcal{SOLUTION:}}}}}}$

$\star{\underline{\blue{\bf{Given:}}}}$

• Dimensions of cuboid are in the ratio of 4 : 3 : 1.
• Total surface area of cuboid = 3800 cm².

$\star{\underline{\blue{\bf{To\;Find:}}}}$

• Volume of Cuboid.

$\star{\underline{\blue{\bf{Formula\;used:}}}}$

• Total surface area of cuboid = 2(LB + BH + HL)
• Volume of cuboid = LBH

Let,

• Length = 4x
• Breadth = 3x
• Height = x

Now,

⇒ Total surface area of cuboid = 2(LB + BH + HL)

⇒ 3800 = 2[(4x) × (3x) + (3x) × (x) + (x) × (4x)]

⇒ 3800 = 2[(12x²) + (3x²) + (4x²)]

⇒ 3800 = 2[19x²]

⇒ 3800 = 38x²

⇒ x² = ${\sf{\dfrac{3800}{38}}}$

⇒ x² = 100

⇒ x = √100

⇒ x = 10 cm

So,

• Length = 4x = 40 cm
• Breadth = 3x = 30 cm
• Height = x = 10 cm

Now, we will find volume of cuboid,

⇒ Volume of cuboid = LBH

⇒ Volume of cuboid = 40 × 30 × 10

⇒ Volume of cuboid = 1200 cm³.

Hence, Volume of cuboid = 1200 cm³.