Question

(ii) How many litres can be contained by a cistern 3 m 5 dm long, 2 m 4 dm wide and 2 m deep​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

Length of cistern = 3 m 5 dm

We know

$\boxed{\rm{  \:1 \: dm \: = \: 0.1 \: m \: }}$

So, using this,

Length of cistern = 3 m 5 dm = 3 + 5 × 0.1 = 3 + 0.5 = 3.5 m

Breadth of cistern = 2 m 4 dm = 2 + 4 × 0.1 = 2 + 0.4 = 2.4 m

Height of cistern = 2 m

We know,

Volume of cuboid of length l, breadth b and height h is given by

$\boxed{\rm{  \: \: Volume_{(Cuboid)} \: = \: l \: \times \: b \: \times \: h \: \: }}$

As cistern is in the shape of cuboid.

So,

$\rm \: Volume_{(Cistern)} = 3.5 \times 2.4 \times 2$

$\rm \: Volume_{(Cistern)} = 7 \times 2.4$

$\rm \: Volume_{(Cistern)} = 16.8 \: {m}^{3}$

We know,

$\boxed{\rm{  \:1 \: {m}^{3} \: = \: 1000 \: litres \: \:}}$

So, using this, we get

$\rm \: Volume_{(Cistern)} = 16.8 \times 1000$

$\rm\implies \:\rm \: Volume_{(Cistern)} = 16800 \: litres$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{CSA_{(cylinder)} = 2\pi \: rh}\\ \\ \bigstar \: \bf{Volume_{(cylinder)} = \pi {r}^{2} h}\\ \\ \bigstar \: \bf{TSA_{(cylinder)} = 2\pi \: r(r + h)}\\ \\ \bigstar \: \bf{CSA_{(cone)} = \pi \: r \: l}\\ \\ \bigstar \: \bf{TSA_{(cone)} = \pi \: r \: (l + r)}\\ \\ \bigstar \: \bf{Volume_{(sphere)} = \dfrac{4}{3}\pi {r}^{3} }\\ \\ \bigstar \: \bf{Volume_{(cube)} = {(side)}^{3} }\\ \\ \bigstar \: \bf{CSA_{(cube)} = 4 {(side)}^{2} }\\ \\ \bigstar \: \bf{TSA_{(cube)} = 6 {(side)}^{2} }\\ \\ \bigstar \: \bf{Volume_{(cuboid)} = lbh}\\ \\ \bigstar \: \bf{CSA_{(cuboid)} = 2(l + b)h}\\ \\ \bigstar \: \bf{TSA_{(cuboid)} = 2(lb +bh+hl )}\\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$