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.
[tex]\longrightarrow{\sf{V_{(Cuboid)} = l \times b \times h}}[/tex]
- ➝ V = Volume
- ➝ l = length
- ➝ b = breadth
- ➝ h = height
[tex]\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}[/tex]
Hence, the value of x is 20.
Now, we know the value of x. So, calculating the dimensions of cuboid :
Length = 3x
Breadth = 2x
Height = x
[tex]\rule{300}{2.5}[/tex]
