Question

The length, breadth and height of a cuboid are in the ratio 1:2:3. If its total surface area is 1100cm², then its volume (in cm³) is-

Answer 1

Pls thanks the answer

Answer 2

Volume of the cuboid is 2121.32 cm³.

• The length , breadth and height of the cuboid are in the ratio 1:2:3.

• Let the common multiple be x.

• Now,

Length of the cuboid (l) = x.

Breadth of the cuboid (b) = 2x

Height of the cuboid (h) = 3x.

• Total surface area f the cuboid is 1100 cm².

• Formula to find the total surface area of the cuboid is 2(lb + bh +hl).

Substituting the values in the formula,

1100 = 2 (2x² + 6x² + 3x²)

550 = 11x²

x² = 50

x = $\sqrt{50}$

• Now the volume of the cuboid is given by length × breadth × height .

Volume  = length × breadth × height

Volume = x × 2x × 3x = 6x³

Volume = 6 (√50)³ = 2121.32 cm³.