Question

the breadth of a room is twice its height and half its length . the volumeof room is 512 m^3.find its dimensions​

Answer 1

✬ Dimensions = 16(8)(4) ✬

Step-by-step explanation:

Given:

• Breadth of a room is twice the height and half of length.
• Volume of room is 512 cm³.

To Find:

• What are the dimensions of room ?

Solution: Let the height be h and length be l. Therefore

➟ Breadth = 2 times of h = 2h

➟ So Height = b/2

also it is given that

➟ Breadth = Length/2

➟ 2(Breadth) = Length

As we know that

★ Volume = Length•Breadth•Height ★

A/q

• Volume is 512 cm³

$\implies{\rm }$ 2b $\times$ b $\times$ b/2 = 512

$\implies{\rm }$ 512 = b³

$\implies{\rm }$ ³√512 = b

$\implies{\rm }$ 8 = b

So, Dimensions are

➫ Breadth is b = 8 cm

➫ Length is 2b = 2(8) = 16 cm

➫ Height is b/2 = 8/2 = 4 cm

Hence, dimensions of room is 16 cm $\times$ 8 cm $\times$ 4 cm

Answer 2

Let ,

The breadth , height and length of a room be " B " ," H " and " L "

Given ,

The breadth of a room is twice its height and half its length

Volume of room = 512 m³

Thus ,

B = 2H => H = B/2

And

B = L/2 => 2B = L

We know that , the volume of cuboid is given by

$\boxed{ \sf{Volume = L × B × H}}$

Thus ,

512 = 2B × B × B/2

(B)³ = 512

B = 3√512

B = 8 m

Therefore ,

• Length (L) = 16 m
• Breadth (B) = 8 m
• Height (H) = 4 m