The volume of a cuboid is 1536 m³. Its length is 16 m, and its breadth and height are in the ratio 3 : 2. Find the breadth and height of the cuboid.

Open in App

Solution

Length of the cuboid = 16 m
Suppose that the breadth and height of the cuboid are 3x m and 2x m, respectively.
$Then 1536 = 16 \times 3 x \times 2 x \Rightarrow 1536 = 16 \times 6 x^{2} \Rightarrow x^{2} = \frac{1536}{96} = 16 \Rightarrow x = \sqrt{16} = 4$

∴ The breadth and height of the cuboid are 12 m and 8 m, respectively.

Suggest Corrections

Similar questions

The volume of a cuboid is 1536 cube m. Its length is 16 m, and its breadth and height are in the ratio 3:2. Find the breadth and height of the cuboid.

Q. The volume of a cuboid is

1536 m^{2}

its length is

60 m

and breadth and height are in ration

3 : 2

find the breadth or height of the cuboid.

Q. The volume of a cuboid is

6400 c u c m

. Its length is

32 c m

, and breadth and height are in the ratio

2 : 1

. Find its breadth and height.

Q. The volume of a cuboid is

24 \sqrt{42} {cm}^{3}

. Its length is

5 \sqrt{2}

cm, breadth and height are in the ratio

\sqrt{3} : \sqrt{7}

. The height of the cuboid is ________.

Q. The volume of a cuboid is given by the product of its length, breadth and height. The length of a cuboid is 2x² times its breadth and the height is

\frac{3}{2}

xy times of length. Find the volume of the cuboid if its breadth is 6y².

Join BYJU'S Learning Program

The volume of a cuboid is 1536 m3. Its length is 16 m, and its breadth and height are in the ratio 3 : 2. Find the breadth and height of the cuboid.

Length of the cuboid = 16 m Suppose that the breadth and height of the cuboid are 3x m and 2x m, respectively. Then 1536=16×3x×2x⇒1536=16×6x2⇒x2=153696=16⇒x=16=4 ∴ The breadth and height of the cuboid are 12 m and 8 m, respectively.

The volume of a cuboid is 1536 m³. Its length is 16 m, and its breadth and height are in the ratio 3 : 2. Find the breadth and height of the cuboid.