Question

The breadth of a room is twice its height and half its length and its volume is 1000 m. Its
dimensions are:
(a) 20 mx 10 mx 5m
(b) 10m x 10 m x 10 m
(c) 40 mx 5 m x 5m
( none of these)​

Answer 1

Question:-

• The breadth of a room is twice its height and half its length and its volume is 1000 m³. Find it's dimensions.

Answer:-

• Option(a): 20m × 10m × 5m

SOLUTION:-

Let the height be x.

Given in the Question,

• Breadth is twice the height but half of the length.
• That means length is twice the breadth
• Volume=1000m³

So breadth will be 2x as height is x (refer to the first line of the solution.) Therefore, Length will be 2*2x that is 4x

$volume = l \times b \times h$

$1000m ^{3} = 4x \times 2x \times x$

$1000 {m}^{3} = 8 {x}^{3}$

$1000m^{3} = (2x)^{3}$

$\sqrt[3]{1000 {m}^{3} } = 2x$

$10m = 2x$

$\frac{10m}{2} = x$

$5m = x$

So we found height =5m

Given in the question,

breadth = twice of height

=2×5m

=10m

length=twice of breadth.

(as mentioned breadth is half of the length)

length=2×10m

=20m

_________________

FINAL ANSWER:-

length=20m

breadth=10m

height = 5m

Therefore correct answer is OPTION (A)