A cuboidal water tank contains 216 litres of water- Its depth is 1-3 of its length and breadth is 1-2 of 1-3 of the difference between length and depth- The length of the tank is

The correct option is B 18 dmLet the length breadth and height of the water #160;in the tank be l, b, h respectively. Then h=1/3l and #160 ...

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Standard VIII

Mathematics

Cube Root Using Prime Factorisation

A cuboidal wa...

Question

A cuboidal water tank contains $216$ litres of water. Its depth is $\frac{1}{3}$ of its length and breadth is $\frac{1}{2}$ of $\frac{1}{3}$ of the difference between length and depth. The length of the tank is

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Solution

The correct option is B $18$ dm
Let the length breadth and height of the water in the tank be $l, b, h$ respectively. Then

$h = \frac{1}{3} l$ and $b = \frac{1}{2}$ of $\frac{1}{3} (l - h)$

$=$ $\frac{1}{2} \times \frac{1}{3} (l - \frac{1}{3} l) = \frac{1}{6} \times \frac{2}{3} l = \frac{1}{9} l$

Given volume of water $= 216$

$\Rightarrow l \times \frac{1}{9} l \times \frac{1}{3} l = 216$

$l^{3} = \frac{216}{1000} \times 27$

$(∵ 1 m^{3} = 1000 l)$

$l = 0.6 \times 3 = 1.8$ m $= (1.8 \times 10)$ dm $= 18$ dm

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A cuboidal water tank contains 216 litres of water. Its depth is 13 of its length and breadth is 12 of 13 of the difference between length and depth. The length of the tank is

The correct option is B 18 dmLet the length breadth and height of the water in the tank be l,b,h respectively. Thenh=13l and b=12 of 13(l−h) = 12×13(l−13l)=16×23l=19lGiven volume of water =216⇒l×19l×13l=216l3=2161000×27 (∵1m3=1000l)l=0.6×3=1.8 m =(1.8×10) dm =18 dm

A cuboidal water tank contains $216$ litres of water. Its depth is $\frac{1}{3}$ of its length and breadth is $\frac{1}{2}$ of $\frac{1}{3}$ of the difference between length and depth. The length of the tank is