Question

The breadth of a room is twice its height and half its length. The volume of the room is 512 cm³. Find the height of the room.

Answer 1

Answer:

The height of the room is 4cm.

Step-by-step explanation:

Given that,

A breadth of a room is twice it's height and half it's length. The volume of the room is 512cm³.

Here, the room is cuboidal-shaped as it is having 3 dimensions.

And also, it's breadth is 2× it's height and ½ of its length. We need to find its height.

Solution :

• As we need to find it's height.

Let's assume it's height as 'x' cm.

Then other dimensions will be :

• breadth = "2x"
• length = "4x" [∵ ½ of 4x is 2x]

We know that,

➙ Volume of a cuboid = l × b × h

But, Volume is 512cm³ (given)

So, we can say that,

→ 512 = x · 2x · 4x

→ 512 = 8x³

→ 512/8 = x³

→ 64 = x³

→ 3√64 = x

→ 4 = x

→ x = 4cm.

Therefore, height of the room is 4cm.

Answer 2

Answer:

Given :-

• The breadth of a room is twice its height and half it's length. The volume of the room is 512 cm³.

To Find :-

• What is the height of the room.

Formula Used :-

↦ Volume of cube = Length × Breadth × Height

Solution :-

Let, the height of the room be h

Again, we take breadth as 2x

And, length as 4x

According to the question by using the formula we get,

⇒ 2x × 4x × x = 512

⇒ 8x³ = 512

⇒ x³ = 512/8

⇒ x³ = 64

⇒ x = √64

➠ x = 4 cm

∴ The height of the room is 4 cm .

Let's Verify :-

↦ 2x × 4x × x = 512

Put x = 4 we get,

↦ 2(4) × 4(4) × 4 = 512

↦ 8 × 16 × 4 = 512

↦ 128 × 4 = 512

↦ 512 = 512

➦ LHS = RHS

Hence, Verified ✔