Question

the volume of a cuboidal vessel is 65cm³.if lenght is double its breadth and four times the height. find the dimensions​

Answer 1

Given:

The volume of a cuboidal vessel is 65cm³

If length is double its breadth and four times the height

To find:

The dimensions​

Solution:

Let's assume,

"L" → the length of the cuboidal vessel

"B" → the breadth of the cuboidal vessel

"H" → the height of the cuboidal vessel

So, according to the question we have,

Length is double the breadth

∴ $B = \frac{L}{2}$ ..... (i)

and

Length is 4 times the height

∴ $H = \frac{L}{4}$ ..... (ii)

We know that,

$\boxed{\bold{Volume\:of\:a\:cuboid = Length\times Breadth\times Height}}$

The volume of the cuboidal vessel = 65 cm³

Therefore, we get an equation as,

$L \times B \times H = 65$

substituting the values from (i) & (ii), we get

$\implies L \times \frac{L}{2} \times \frac{L}{4} = 65$

$\implies L^3 = 65 \times 2 \times 4$

$\implies L^3 = 520$

$\implies L = \sqrt[3]{520}$

$\implies \bold{L}$ ≈ $\bold{8.04}$

∴ B = $\frac{L}{2} = \frac{8.04}{2} = \bold{4.02}$

and

∴ H = $\frac{L}{4} = \frac{8.04}{4} = \bold{2.01}$

Thus, the dimensions of the cuboidal vessel is:

$\boxed{\bold{Length \:\rightarrow\underline{8.04\:cm}}}\\\\\boxed{\bold{Breadth \:\rightarrow\underline{4.02\:cm}}}\\\\\boxed{\bold{Height \:\rightarrow\underline{2.01\:cm}}}$

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