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:

Let x be the height of the room Its breadth is therefore 2x and length 4x.

volume of the cube = 2x×4x×x

8x³ = 512 cubic meters

x =4cm

so the height of room =4cm

Answer 2

Answer ::

The height of the room is 4cm.

Step-by-step explanation ::

To Find:-

• The height of the room

Solution:-

Given that,

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

Let us assume the length, breadth and the height as ::

➻ Height

Let us assume the height of the room as x,

➻ Length & Breadth

As it is said, the breadth of the room is twice the height and half it's length, therefore let us assume the breadth and length are 2x and 4x,

ACCORDING THE QUESTION,

The height of the room is,

As we know that,

$\dag \: \underline{ \boxed{ \sf{\red{Volume \: of \: cuboid \: = l \times b \times h}}}}$

Therefore,

⟿ l × b × h = 512

⟿ 4x × 2x × x = 512

⟿ 8x² × x = 512

⟿ 8x³ = 512

⟿ x³ = 512 / 8

⟿ x³ = 64

⟿ x = 4 × 4 × 4

⟿ x = 4 ★

The height of the room is,

We assumed the height of the room as x,

⟿ x

⟿ 4 cm ★

The height of the room is 4cm.