Question

$\huge\tt\fcolorbox{blue}{red}{ QUESTION}$

ᴀ ᴡᴀᴛᴇʀ ᴛᴀɴᴋ ʜᴀꜱ ᴛʜᴇ ꜱʜᴀᴘᴇ ᴏꜰ ᴀ ʀᴇᴄᴛᴀɴɢᴜʟᴀʀ ᴘʀɪꜱᴍ ᴏꜰ ʙᴀꜱᴇ 50 ᴄᴍ². ᴛʜɪꜱ ᴛᴀɴᴋ ɪꜱ ʙᴇɪɴɢ ꜰɪʟʟᴇᴅ ᴀᴛ ᴛʜᴇ ʀᴀᴛᴇ ᴏꜰ 12 ʟɪᴛᴇʀꜱ ᴘᴇʀ ᴍɪɴᴜᴛᴇꜱ. ꜰɪɴᴅ ᴛʜᴇ ʀᴀᴛᴇ ᴀᴛ ᴡʜɪᴄʜ ᴛʜᴇ ʜᴇɪɢʜᴛ ᴏꜰ ᴛʜᴇ ᴡᴀᴛᴇʀ ɪɴ ᴛʜᴇ ᴡᴀᴛᴇʀ ᴛᴀɴᴋ ɪɴᴄʀᴇᴀꜱᴇꜱ; ᴇxᴘʀᴇꜱꜱ ʏᴏᴜʀ ᴀɴꜱᴡᴇʀ ɪɴ ᴍɪʟʟɪᴍᴇᴛᴇʀꜱ ᴘᴇʀ ꜱᴇᴄᴏɴᴅ.

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Answer 1

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Given :- A water tank has the shape of a rectangular prism of base 50 cm². This tank is been filled at the rate of 12 litres per minute. Find the rate at which the height of the water in the water tank increases. Express your answer in mm per second.

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To Find :- Here, in the given question, we have to find the rate at which the height of the water in the water tank increases in mm/s.

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Taken :-

• Let V = volume of water at time t
• h = depth of water at time t

And,

$\sf\dfrac{ dV}{dt}$ = 1 L/min = 1000 cm³/min.

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Solution :-

The volume of water at time t is;

• V = (area of base)(height)
• V = 100h

» Differentiate with respect to t to get $\sf\dfrac{dV}{dt}$ = 100($\sf\dfrac{dh}{dt}$)

So,

• $\bf\dfrac{dh}{dt}$ = ($\sf\dfrac{1}{100}$)($\sf\dfrac{dV}{dt}$)
• ⇒ ($\sf\dfrac{1}{100}$)(1000) = 10 cm/min.

Now, to convert the given equation to mm/s, we will,

We know that;

• 1 cm = 10 milimeter.
• 1 min = 60 s.

Thus,

• 10 cm/min
• ⟼ 1.66666667 mm/s.

~Hence, the rate at which the height of the water in the water tank increases in mm/s will be 1.66666667 mm/s.

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Answer 2

Answer:

Given :-

A water tank has the shape of a rectangular prism of base 50 cm².

This tank is been filled at the rate of 12 litres per minute.

Find the rate at which the height of the water in the water tank increases.

Express your answer in mm per second.

Answer in attachment :)