Question

The breadth of a room is twice its height and is half of its length. The volume of room is 512cu.m.Its height is _______

Answer 1

Answer:

1024 hight

Step-by-step explanation:

please mark me as brainliest first

Answer 2

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Concept}}}$

Here the Concept of Cuboid has been used. We know that room is always in the shape of cuboid. Here the volume has been given of cuboid. We see that all the sides are made to depend on each other. So firstly we shall make relationship between all the sides and volume. After that we will find the one side and from it we can find other sides.

Let's do it !!

______________________________________________

★ Formula Used :-

$\\\;\boxed{\sf{\pink{Length\:\times\:Breadth\:\times\:Height\;=\;\bf{Volume\:of\:Cuboid}}}}$

______________________________________________

★ Solution :-

Given,

» Breadth of room = 2 × Height

» Breadth of room = ½ × Length

» Volume of room = 512 m³

• Let the height of the room be 'H'

• Let the length of the room be 'L'

• Let the breadth of the room be 'B'

Then according to the given things,

» B = 2h

» B = ½ × L

→ L = 2B = 2(2H) = 4 H

So we got the dimensions of the room.

• Length of room = 4H

• Breadth of room = 2H

• Height of room = H

Now using the formula of Volume of Cuboid, we get

$\\\;\sf{:\rightarrow\:\;Length\:\times\:Breadth\:\times\:Height\;=\;\bf{Volume\:of\:Cuboid_{(Room)}}}$

Now equating the values, we get

$\\\;\sf{:\Longrightarrow\:\;4H\:\times\:2H\:\times\:H\;=\;\bf{512}}$

$\;\sf{:\Longrightarrow\:\;8\:H^{3}\;=\;\bf{512}}$

$\\\;\sf{:\Longrightarrow\:\;H^{3}\;=\;\bf{\dfrac{512}{8}}}$

$\\\;\sf{:\Longrightarrow\:\;H^{3}\;=\;\bf{64}}$

$\\\;\sf{:\Longrightarrow\:\;H\;=\;\bf{\sqrt[3]{64}}}$

$\\\;\sf{:\Longrightarrow\:\;H\;=\;\bf{\sqrt[3]{4\:\times\:4\:\times\:4}}}$

$\\\;\bf{:\Longrightarrow\:\;H\;=\;\bf{\red{4\;\:m}}}$

Hence, Height of the room = 4 m

Now using this height we get,

→ Length of room = L = 4(H) = 4(4) = 16 m

→ Breadth of room = B = 2(H) = 2(4) = 8 m

$\\\;\underline{\boxed{\tt{Height\;\:of\;\:room\;=\;\bf{\purple{4\;\:m}}}}}$

______________________________________________

★ Verification of the Answer :-

In order to verify, we need to simply apply the values we got into the equation we formed. Then,

$\\\;\tt{\gray{:\mapsto\:\;Length\:\times\:Breadth\:\times\:Height\;=\;\bf{Volume\:of\:Cuboid_{(Room)}}}}$

$\\\;\tt{\gray{:\mapsto\:\;4H\:\times\:2H\:\times\:H\;=\;512}}$

$\\\;\tt{\gray{:\mapsto\:\;16\:\times\:8\:\times\:4\;=\;512}}$

$\\\;\tt{\gray{:\mapsto\:\;512\;=\;512}}$

$\\\;\tt{\orange{:\mapsto\:\;512\;cm^{3}\;=\;512\;cm^{3}}}$

Clearly LHS = RHS. So our answer is correct. Hence, Verified.

______________________________________________

★ More to know about Cuboid :-

$\\\;\sf{\leadsto\;\;CSA\;of\;Cuboid\;=\;2(L\:+\:B)\:\times\:H}$

$\\\;\sf{\leadsto\;\;TSA\;of\;Cuboid\;=\;2(LB\:+\:BH\:+\:LH)}$

$\\\;\sf{\leadsto\;\;Diagonal\;of\;Cuboid\;=\;\sqrt{(L^{2}\:+\:B^{2}\:+\:H^{2})}}$