Question

The length of a cuboid is twice the breadth and thrice the height. If the volume of the cuboid is 974cmcub, find the dimensions of the cuboid​

Answer 1

Question:

The length of a cuboid is twice the breadth and thrice the height. If the volume of the cuboid is $974cm^{3}$, find the dimensions of the cuboid.

Solution:

Given :

A cuboid, whose area is $\bold{974cm^{3}}$

*Length = 2 $\times$ Breadth (2B)= 3 $\times$ Hieght (3H)

*Hieght = $2B = 3H => H = \bold{\frac{2B}{3}}$

Breadth => B

So, finally we have :

L = 2B

B = B

H = $\bold{\frac{2B}{3}}$

Formula of Volume of Cuboid = L X B X H

According, to the question:

$974cm^{3} = 2B \times B \times \frac{2B}{3} \\ => 974cm^{3} = \frac{4B^{3}}{3} \\ => B^{3} = \frac{974 \times 3}{4} \\=> B^{3} = 730.5 \\=> B = 3 \sqrt{730.5} \\=>B = 9cm\:\:(approx.)$

So,

L = $2B = 2\times 9$ = 18cm

B = 9cm

H = $\frac{2B}{3} = \frac{2\times 9}{3}$ = 6cm

Hence, the dimensions of the Cuboid are 18cm, 9cm, 6cm.

Answer 2

Answer:

the dimensions of the cuboid are 18cm, 9cm, 6cm .