Question

17) The breath of a room is twice its height and half its length. The volume
of the room is 512 m3. The length of the room is
O 12 m
O 14 m
O 16 m
O 18 m​

Answer 1

${ \underline{ \underline{ \tt{ \huge{Question}}}}} :$

• The breath of a room is twice its height and half its length. The volume of the room is 512 m3. The length of the room is

${ \underline{ \underline{ \tt{ \huge{To \: \: Find}}}}} :$

• Find the length of the room.

${ \underline{ \underline{ \tt{ \huge{Given}}}}} :$

• The breath of a room is twice its height and half its length. The volume of the room is 512 m³.

${ \underline{ \underline{ \tt{ \huge{Solution}}}}} :$

• Let the height be " x "

• Breadth is " 2x "

• Length is " 4x "

• Volume is " 512 m³ "

${ \implies{ \tt{Volume = Length \times Breadth \times Height}}}$

${ \implies{ \tt{512 = 4x \times 2x \times x}}}$

${ \implies{ \tt{512 = { 8x }^{ 3 } }}}$

${ \implies{ \tt{ { x }^{ 3 } = \cancel\dfrac { 512 } { 8 } }}}$

${ \implies{ \tt{ { x }^{ 3 } = 64}}}$

${ \implies{ \tt{a = 2}}}$

Hence ,

• Length is 4x = 16 m

• Breadth is 2x = 8 m

• Height is x = 4 m

Answer 2

Given
=>Volume of the room = 512m^3

=>breadth (b) of the room = 2* height (h)
=> b = 2h
=> h = 1/2*b


=>breadth (b) of the room = 1/2 * length (l)
=> b = 1/2*l
=> l = 2*b

Solution
Volume of the room = l*b*h

=>512 = 2b* b * 1/2 b
=>512 = b* b * b
=>512 = b^3
=>b = 8 m

The length of the room = 2b
= 2*8
= 16 m