Question

the length of a cuboid is 3 times of it's height and it's breadth is 2 times it's height if the volume of the cuboid is 48000cm cube, calculate it's dimensions​

Answer 1

Answer:

The length, breadth and height of cuboid are 60 cm, 40 cm and 20 cm.

Step-by-step explanation:

Let,

• The height of cuboid be X cm.
• The length of cuboid is three times of it's height. So, it will be 3x.
• The breadth of cuboid is two times of it's height. So, it will be 2x.

Now, substuting all the given values in the formula to find the value of x.

$\longrightarrow{\sf{V_{(Cuboid)} = l \times b \times h}}$

• ➝ V = Volume
• ➝ l = length
• ➝ b = breadth
• ➝ h = height

$\begin{gathered} \qquad\longrightarrow{\sf{V_{(Cuboid)} = l \times b \times h}}\\\\\qquad\longrightarrow{\sf{48000 = 3x \times 2x \times x}}\\\\\qquad\longrightarrow{\sf{48000 = 3x \times 2{x}^{2}}}\\\\\qquad\longrightarrow{\sf{48000 = 6{x}^{3}}}\\\\\qquad\longrightarrow{\sf{{x}^{3} = \dfrac{48000}{6}}}\\\\\qquad\longrightarrow{\sf{{x}^{3} = 8000}}\\\\\qquad\longrightarrow{\sf{x = \sqrt[3]{8000}}}\\\\\qquad\longrightarrow{\sf{x = 20}}\\\\ \qquad{\star{\underline{\boxed{\sf{\purple{x = 20}}}}}} \end{gathered}$

Hence, the value of x is 20.

Now, we know the value of x. So, calculating the dimensions of cuboid :

Length = 3x

• ➝ 3 × 20
• ➝ 60 cm

Breadth = 2x

• ➝ 2 × 20
• ➝ 40 cm

Height = x

• ➝ 1 × 20
• ➝ 20 cm

$\rule{300}{2.5}$